Intelligent Medical Diagnosis Reasoning Using Composite Fuzzy Relation, Aggregation Operators and Similarity Measure of q-Rung Orthopair Fuzzy Sets

Abstract

Medical diagnosis is the process of finding out what is the disease a person may be suffering from. From the symptoms and their gradation, the doctor can decide which the dominant disease is. Nevertheless, in the process of medical diagnosis, there is ambiguity, uncertainty, and a lack of medical knowledge that can adversely affect the doctor’s judgment. Thus, a tool of artificial intelligence, fuzzy logic, has come to enhance the decision-making of diagnosis in a medical environment. Fuzzy set theory uses the membership degree to characterize the uncertainty and, therefore, fuzzy sets are integrated into imperfect data in order to make a reliable diagnosis. The patient’s medical status is represented as q-rung orthopair fuzzy values. In this paper, many versions and methodologies were applied such as the composite fuzzy relation, fuzzy sets extensions (q-ROFS) with aggregation operators, and similarity measures, which were proposed as decision-making intelligent methods. The aim of this procedure was to find out which of the diseases (viral fever, malaria fever, typhoid fever, stomach problems, and chest problems), was the most influential for each patient. The work emphasizes the contribution of aggregation operators in medical data in order to contain more than one expert’s aspect. The performance of the methodology was quite good and interesting as most of the results were in agreement with previous works.

1. Introduction

1.1. Background

Medical diagnosis is the process of finding the disease from the symptoms the patient is experiencing. However, medical data is often uncertain and difficult to retrieve. Moreover, the relationship between symptoms and disease depends on uncertain information that influences the decision-making process [1]. Fuzzy sets by Zadeh have been applied in the past for many medical applications. This framework provides a way to overcome problems in which imprecision, absence of sharply defined criteria, and incomplete or uncertain data, are involved [2]. Fuzzy logic has a significant role in medical science due to its complexity. Applications like cardiology, endocrinology, urology, ophthalmology, and dentistry are some of the numerous medical fields in which fuzzy logic is applied [3]. Also, the concept of fuzzy logic deals with problems including pattern recognition, medical diagnosis, and decision-making [4]. Thus, the ambition of using fuzzy logic in medicine is to generate results like an expert and diagnose the patients at an early stage [3]. Nevertheless, the theory of Zadeh about fuzzy sets is limited in the sense that it is defined by membership grade only [4]. So, the inevitable presence of uncertainty in the real world as well as the limitation of fuzzy set theory by Zadeh, led to extensions of fuzzy sets (advanced fuzzy sets), which cope with imprecision and vagueness more successfully and accurately than fuzzy sets by Zadeh [5]. The extensions of fuzzy sets are defined by the degree of membership, degree of non-membership, and degree of indeterminacy, and include intuitionistic fuzzy sets (IFSs), Pythagorean fuzzy sets (PFSs), and Fermatean fuzzy sets (FFSs). The concepts of these fuzzy sets are all generalized as q-rung orthopair fuzzy sets (q-ROFS) [4]. Fuzzy logic also uses similarity measures for disease detection.

1.2. Related Works

Fuzzy sets have been applied in the past to solve many medical applications. They have also been applied in various ways. Using neuroimaging and hierarchical fuzzy models, a computational model for the diagnosis of burnout was constructed. Burnout is complex enough to study, but by using artificial intelligence tools it can be approximated and diagnosed [6]. A more extended application concerning medical diagnosis is to find the disease corresponding to a patient given fuzzy relations. There are various ways of using fuzzy sets in making a medical decision. Zadeh extended the theory of fuzzy sets by introducing the Z-numbers. A Z-number is an ordered pair of fuzzy numbers that restricts the reliability and evaluation of human judgment. The first fuzzy number is the uncertainty of information in evaluation and the second fuzzy number represents the reliability. Z-numbers have been applied to medical diagnosis problems. However, a more distinct study for Z-number weights is needed, as well as the idea of a negative human-decision approach is necessary to be incorporated [7]. In [8], a formula named compositional rule of inference (CRI) has been applied to fuzzy sets for making a medical decision. In this case, the term “multi-criteria” is introduced by extracting a result through many components. Another formula using multi-criteria is the Preference ranking organization method for the enrichment of evaluation (PROMETHEE) [9]. This method can cope with complex and multiple criteria, and it depends on the information and the weight of the criteria. The PROMETHEE model can be extended to cope with incomplete weight information. In [4,5,10,11], decision-making must be taken by q-ROFS and applying Sanchez’s approach. This method uses fuzzy relations and compositions in order to achieve the medical diagnosis; it is a method that solves multi-criteria problems as well [9]. In [12,13], more complicated forms of fuzzy sets are mentioned, adapting human language more effectively. Bipolar fuzzy sets [12] are complex sets that cope with positive and negative human opinions, while picture fuzzy sets [13] consist of three parameters: positive degree, neutral degree, and negative degree. The concept of spherical fuzzy sets (SFSs) [14] is an extension of PFSs which includes three degrees, membership, abstinence, and non-membership, and it is more flexible than q-ROFSs. Distance is another method in order to make a medical decision. Pattern recognition uses distances and similarity measures to estimate which pattern is closer to a specific class (like a disease). Szmidt and Kacprzyk [11] used Euclidean and Hamming distances which are the most common distances for classification and pattern recognition. In [15], a new distance measure is introduced. Using matrix norms, this distance measure has better performance than the common distances. Other distance measures are presented in [16]. FFSH distance is based on the Hellinger distance and FFSTD distance is based on the triangular divergence. These distances are applied to q-ROFS for q = 3 (FFS) and have a better performance as well. In [17,18,19], an alternative measure is proposed. Divergence measures for advanced fuzzy sets (q-ROFS) have played an important role in decreasing uncertainty and making decision-making with optimum accuracy [17]. Divergence measures are distances with divergence perspective and, thus, the larger the divergence measure distance, the more different objects (fuzzy sets), and the smaller the divergence measure distance, the more similar objects (fuzzy sets) [18]. In [17], a parametric intuitionistic fuzzy divergence measure (PIFDM distance) was analyzed. (PFSDM distance) was analyzed, in [18] a divergence measure of PFSs (PFSDM distance) was analyzed, and in [19] the Jensen-Shannon divergence of PFSs (PFSJS distance) was analyzed. In general, divergence measures have to be used for more applications such as pattern recognition and multi-criteria decision-making problems. Similarity measures are another tool that plays an important role in many majors such as machine learning, medical diagnosis, and pattern recognition. Similarity measures quantify the similarity or distance between two or more objects, which assist the observer in comparing a group of objects based on their traits [12,20]. These measures are developed using fuzzy sets and extended fuzzy sets (q-ROFS) [20]. In most cases, similarity measures have been developed by distances [21]. Wei, Wei, and Ye [21,22] proposed similarity measures based on a cosine function using advanced fuzzy sets for making a medical decision. Muthukumar and Krishnan [20] used weighted similarity measures in medical diagnosis, while Iancu [23] used similarity measures based on the Frank t-norms family. Mahmood, Jaleel, and Rehman [12] used trigonometric similarity measures in bipolar fuzzy sets, while Albaity and Mahmood [24] used generalized dice similarity measures in pattern recognition and medical diagnosis problems. Nonetheless, similarity measures need to be involved in more complex decision-making problems with risk, and many other fields under uncertainty [21].

1.3. Problem Statement and Objective

The novelty and contribution of this work relied on the combination of various techniques for intelligent medical diagnosis reasoning. In this paper, the data were derived from [4,5,10,11,17,18,23], where there were four patients and the following diseases: viral fever, malaria fever, typhoid fever, stomach problems, and chest problems. In these data, various ways were applied for a reliable diagnosis. The applied methods were as follows. First, composite fuzzy relations with min-max-min and max-average-min-average using different relation value types were studied in intuitionistic fuzzy sets. Moreover, the q-ROFs with q-rung separately using aggregation operators, was another method. A value of Q = 1 gives the IFSs, q = 2, gives the PFSs, and q = 3, gives the FFSs. It is very important that the estimation by an expert be re-examined or completed. This results in a more reliable source of data that includes more than one medical opinion. So, the data should be combined with other data which considers the other expert’s opinion. This fusion is to be implemented through aggregation operators and, thus, the best possible result for the diagnosis of the patient is achieved. Aggregation operators (Arithmetic Mean, Harmonic Mean, Bellman-Zadeh, I-OWA, q-ROFWA) were used, for medical examination and patient’s history. It has been observed that q-ROFs could better designate fuzziness. Lastly, the similarity measures were applied in fuzzy sets to evaluate a brief procedure. These measures were based on cosine measures and Peng measures for IFS, as well as q-ROFC measures for IFS, PFS, and FFS. The procedure of medical diagnosis is summarized in Section 2.12. One of the novelties of this paper is that it used several methods such as similarity measures and composite fuzzy relations, in the same data. The most important innovation was that a second opinion from an expert on the patient’s symptoms was used and integrated with the first opinion through the aggregation operators. By applying aggregation operators, many opinions can be combined in one and, thus, the decision was more accurate. This paper is organized as follows. Section 2 outlines the theory of fuzzy sets and advanced fuzzy sets. It also contains the mathematical formulas, the various methods for decision-making, including similarity measures and composite fuzzy relations, the mathematical formulas for decision-making, including relation values and score with accuracy, the aggregation operators and the medical data, and the algorithm with a flowchart. Section 3 presents the results and the discussion. Finally, Section 4 summarizes the paper with recommendations for future research.

2. Materials and Methods

2.1. Fuzzy Sets

A fuzzy set is a class of objects with a continuum of grades of membership. A fuzzy set was introduced by Lotfi Zadeh [2]. Let $\mathrm{X}$ be a space of objects $\mathrm{x}$. According to Zadeh, a fuzzy set $\mathrm{A}$ of $\mathrm{X}$ is characterized by a membership function:

$$\mathrm{A}=\left\{〈\mathrm{x},{\mathsf{\mu }}_{\mathsf{A}}\left(\mathrm{x}\right)〉\right|\mathrm{x}\mathsf{ϵ}\mathrm{X}\}$$

(1)

where the function ${\mathsf{\mu }}_{\mathsf{A}}\left(\mathrm{x}\right):\mathrm{X}⟶[0,1]$ defines the degree of membership of the element $\mathrm{x}\in \mathrm{X}$. $\mathrm{X}$ is the nonempty set [2,5].

2.2. Intuitionistic Fuzzy Sets (IFS)

Atanassov [25] introduced the expansion of classic fuzzy sets, expressing the fuzzy sets in a different way. An intuitionistic fuzzy set (by Atanassov) $\mathrm{A}$ of $\mathrm{X}$ is given by:

$$\mathrm{A}=\{\langle \mathrm{x},{\mathsf{\mu }}_{\mathsf{A}}\left(\mathrm{x}\right),{\mathsf{\nu }}_{\mathsf{A}}(\mathrm{x})\rangle |\mathrm{x}\mathsf{ϵ}\mathrm{X}\}$$

(2)

where ${\mathsf{\mu }}_{\mathsf{A}}\left(\mathrm{x}\right):\mathrm{X}⟶[0,1]$ and ${\mathsf{\nu }}_{\mathsf{A}}\left(\mathrm{x}\right):\mathrm{X}⟶[0,1]$ such that

$$0\le {\mathsf{\mu }}_{\mathsf{A}}\left(\mathrm{x}\right)+{\mathsf{\nu }}_{\mathsf{A}}\left(\mathrm{x}\right)\le 1$$

(3)

and ${\mathsf{\mu }}_{\mathsf{A}}$ defines the degree of membership, and ${\mathsf{\nu }}_{\mathsf{A}}$ defines the degree of non-membership [4,11,25]. There also another factor that defines an intuitionistic fuzzy set, the degree of indeterminacy

$${\mathsf{\pi }}_{\mathsf{A}}\left(\mathrm{x}\right)=1-{\mathsf{\mu }}_{\mathsf{A}}\left(\mathrm{x}\right)-{\mathsf{\nu }}_{\mathsf{A}}\left(\mathrm{x}\right)$$

(4)

where ${\mathsf{\pi }}_{\mathsf{A}}\left(\mathrm{x}\right)$ expresses the hesitation degree of whether $\mathrm{x}$ belongs to $\mathrm{A}$ or not. It is clear that $0\le {\mathsf{\pi }}_{\mathsf{A}}\left(\mathrm{x}\right)\le 1$ [4,11].

2.3. Pythagorean Fuzzy Sets (PFS)

Yager [26] defined the Pythagorean fuzzy set which is a set of the same functions as the intuitionistic fuzzy set. A Pythagorean fuzzy set $\mathrm{A}$ of $\mathrm{X}$ is given by:

$$\mathrm{A}=\{\langle \mathrm{x},{\mathsf{\mu }}_{\mathsf{A}}\left(\mathrm{x}\right),{\mathsf{\nu }}_{\mathsf{A}}(\mathrm{x})\rangle |\mathrm{x}\mathsf{ϵ}\mathrm{X}\}$$

(5)

where ${\mathsf{\mu }}_{\mathsf{A}}\left(\mathrm{x}\right):\mathrm{X}⟶[0,1]$ and ${\mathsf{\nu }}_{\mathsf{A}}\left(\mathrm{x}\right):\mathrm{X}⟶[0,1]$, but the condition here is: $0\le {{\mathsf{\mu }}_{\mathsf{A}}\left(\mathrm{x}\right)}^2+{{\mathsf{\nu }}_{\mathsf{A}}\left(\mathrm{x}\right)}^2\le 1,$ and ${\mathsf{\mu }}_{\mathsf{A}}$ defines the degree of membership, and ${\mathsf{\nu }}_{\mathsf{A}}$ defines the degree of non-membership. Supposing

$$0\le {{\mathsf{\mu }}_{\mathsf{A}}}^2\left(\mathrm{x}\right)+{{\mathsf{\nu }}_{\mathsf{A}}}^2\left(\mathrm{x}\right)\le 1$$

(6)

the degree of indeterminacy of $\mathrm{x}\in \mathrm{X}$ of $\mathrm{A}$ changes to:

$${\mathsf{\pi }}_{\mathsf{A}}\left(\mathrm{x}\right)={\left(1-{{\mathsf{\mu }}_{\mathsf{A}}}^2\left(\mathrm{x}\right)-{{\mathsf{\nu }}_{\mathsf{A}}}^2\left(\mathrm{x}\right)\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$$

(7)

and ${\mathsf{\pi }}_{\mathsf{A}}\left(\mathrm{x}\right)\in \left[\mathrm{0,1}\right]$ [4,5].

2.4. Fermatean Fuzzy Sets (FFS)

Fermatean fuzzy sets [27] introduced by Yager and this kind of fuzzy sets have the same functions as previously mentioned. A Fermatean fuzzy set $\mathrm{A}$ of $\mathrm{X}$ is given by

$$\mathrm{A}=\{\langle \mathrm{x},{\mathsf{\mu }}_{\mathsf{A}}\left(\mathrm{x}\right),{\mathsf{\nu }}_{\mathsf{A}}(\mathrm{x})\rangle |\mathrm{x}\mathsf{ϵ}\mathrm{X}\}$$

(8)

where ${\mathsf{\mu }}_{\mathsf{A}}\left(\mathrm{x}\right):\mathrm{X}⟶\left[0,1\right]$ and ${\mathsf{\nu }}_{\mathsf{A}}\left(\mathrm{x}\right):\mathrm{X}⟶\left[0,1\right],$ but the relation between ${\mathsf{\mu }}_{\mathsf{A}}\left(\mathrm{x}\right)$ and ${\mathsf{\nu }}_{\mathsf{A}}\left(\mathrm{x}\right)$ is different:

$$0\le {{\mathsf{\mu }}_{\mathsf{A}}}^3\left(\mathrm{x}\right)+{{\mathsf{\nu }}_{\mathsf{A}}}^3\left(\mathrm{x}\right)\le 1$$

(9)

where ${\mathsf{\mu }}_{\mathsf{A}}$ defines the degree of membership and ${\mathsf{\nu }}_{\mathsf{A}}$ defines the degree of non-membership. The degree of indeterminacy of $\mathrm{x}\in \mathrm{X}$ of $\mathrm{A}$ is:

$${\mathsf{\pi }}_{\mathsf{A}}\left(\mathrm{x}\right)={\left(1-{{\mathsf{\mu }}_{\mathsf{A}}}^3\left(\mathrm{x}\right)-{{\mathsf{\nu }}_{\mathsf{A}}}^3\left(\mathrm{x}\right)\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$$

(10)

and ${\mathsf{\pi }}_{\mathsf{A}}\left(\mathrm{x}\right)\in \left[\mathrm{0,1}\right]$ [4,27].

2.5. q-Rung Orthopair Fuzzy Sets (q-ROFs)

Now, the generalized aspect of the previous fuzzy sets was introduced. The idea of qth rung orthopair fuzzy sets (q-ROFs) expands the abilities of fuzzy sets. First, a qth rung orthopair fuzzy subset $\mathrm{A}$ of $\mathrm{X}$ is given by:

$$\mathrm{A}=\{\langle \mathrm{x},{\mathsf{\mu }}_{\mathsf{A}}\left(\mathrm{x}\right),{\mathsf{\nu }}_{\mathsf{A}}(\mathrm{x})\rangle |\mathrm{x}\mathsf{ϵ}\mathrm{X}\}$$

(11)

where ${\mathsf{\mu }}_{\mathsf{A}}\left(\mathrm{x}\right):\mathrm{X}⟶[0,1]$ and ${\mathsf{\nu }}_{\mathsf{A}}\left(\mathrm{x}\right):\mathrm{X}⟶\left[0,1\right],$ and ${\mathsf{\mu }}_{\mathsf{A}}$ defines the degree of membership and ${\mathsf{\nu }}_{\mathsf{A}}$ defines the degree of non-membership [4,28]. Due to its generalization, the commitment between ${\mathsf{\mu }}_{\mathsf{A}}\left(\mathrm{x}\right)$ and ${\mathsf{\nu }}_{\mathsf{A}}\left(\mathrm{x}\right)$ is:

$$0\le {{\mathsf{\mu }}_{\mathsf{A}}}^{\mathrm{q}}\left(\mathrm{x}\right)+{{\mathsf{\nu }}_{\mathsf{A}}}^{\mathrm{q}}\left(\mathrm{x}\right)\le 1$$

(12)

and the degree of indeterminacy is:

$${\mathsf{\pi }}_{\mathsf{A}}\left(\mathrm{x}\right)={(1-{{\mathsf{\mu }}_{\mathsf{A}}}^{\mathrm{q}}\left(\mathrm{x}\right)-{{\mathsf{\nu }}_{\mathsf{A}}}^{\mathrm{q}}\left(\mathrm{x}\right))}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{q}$}\right.}$$

(13)

where $\mathrm{q}\ge 1$ [4,28].

As it is noticed, $\mathrm{q}=1$ corresponds to Atanassov’s IFS, $\mathrm{q}=2$ corresponds to Yager’s PFS, and $\mathrm{q}=3$ corresponds to Yager’s FFS [28]. As $\mathrm{q}$ increases the space of acceptable orthopairs (${\mathsf{\mu }}_{\mathsf{A}}\left(\mathrm{x}\right)$ and ${\mathsf{\nu }}_{\mathsf{A}}\left(\mathrm{x}\right)$) increases, there is less strength of commitment (Equation (12)) [27,28]. For example, the space of Pythagorean membership grades is greater than the space of intuitionistic membership grades [26,28]. Figure 1 represents the available pairs of ${\mathsf{\mu }}_{\mathsf{A}}\left(\mathrm{x}\right)$ and ${\mathsf{\nu }}_{\mathsf{A}}\left(\mathrm{x}\right)$ for various values of q.

2.6. Extension Sanchez’s Method (Composite Fuzzy Relation 1, CFR1)

The extension of Sanchez’s method (DBR) [29] for medical diagnosis is the major way to extract a composite fuzzy relation and it is very useful in medical diagnosis.

Let two non-empty sets be ${\mathrm{p}}_{\mathrm{l}}$ where $\mathrm{l}\in \left\{1,\dots ,\mathrm{L}\right\}$, and ${\mathrm{s}}_{\mathrm{j}}$, where $\mathrm{j}\in \left\{1,\dots ,\mathrm{n}\right\}$. A fuzzy relation $\mathrm{Q}$ from ${\mathrm{p}}_{\mathrm{l}}$ to ${\mathrm{s}}_{\mathrm{j}}$ is a fuzzy set of $\mathrm{P}\times \mathrm{S}$, characterized by ${\mathsf{\mu }}_{\mathrm{Q}}$ and ${\mathsf{\nu }}_{\mathrm{Q}}$ [5].

Let two non-empty sets be ${\mathrm{s}}_{\mathrm{j}}$ where $\mathrm{j}\in \left\{1,\dots ,\mathrm{n}\right\},$ and ${\mathrm{d}}_{\mathrm{m}}$ where $\mathrm{m}\in \left\{1,\dots ,\mathrm{M}\right\}$. A fuzzy relation $\mathrm{R}$ from ${\mathrm{s}}_{\mathrm{j}}$ to ${\mathrm{d}}_{\mathrm{m}}$ is a fuzzy set of $\mathrm{S}\times \mathrm{D}$, characterized by ${\mathsf{\mu }}_{\mathrm{R}}$ and ${\mathsf{\nu }}_{\mathrm{R}}$ [5].

Let $\mathrm{Q}(\mathrm{P}⟶\mathrm{S})$ and $\mathrm{R}(\mathrm{S}⟶\mathrm{D})$ be two fuzzy relations. We define $\mathrm{T}=\mathrm{R}\circ \mathrm{Q}$, $\mathrm{T}\in (\mathrm{P}\times \mathrm{D}),$ and the-composite fuzzy relation of $\mathrm{R}$ and $\mathrm{Q}$, by $\left(\mathrm{R}\circ \mathrm{Q}\right)\left(\mathrm{p},\mathrm{d}\right)=\underset{\mathrm{s}}{\bigvee }\left[\mathrm{Q}\left(\mathrm{p},\mathrm{s}\right)\mathrm{\bigwedge }\mathrm{R}(\mathrm{s},\mathrm{d})\right]$ or

$${\mathsf{\mu }}_{\mathrm{T}}\left({\mathrm{p}}_l,{\mathrm{d}}_{\mathrm{m}}\right)=\underset{\mathrm{s}\in \mathrm{S}}{\bigvee }\left[{\mathsf{\mu }}_{\mathrm{Q}}\right({\mathrm{p}}_{\mathrm{m}},{\mathrm{s}}_{\mathrm{j}}\left)\mathrm{\bigwedge }{\mathsf{\mu }}_{\mathrm{R}}\right({\mathrm{s}}_{\mathrm{j}},{\mathrm{d}}_{\mathrm{m}}\left)\right]$$

(14)

where $\mathrm{s}\in \mathrm{S},$ for all $(\mathrm{p},\mathrm{d})\in \mathrm{P}\times \mathrm{D}$, $\mathrm{\bigvee }=\mathrm{m}\mathrm{a}\mathrm{x}$ and $\mathrm{\bigwedge }=\mathrm{m}\mathrm{i}\mathrm{n}$, ${\mathrm{p}}_{\mathrm{l}}$ = patient for $l=1\dots \mathrm{L}$, ${\mathrm{d}}_{\mathrm{m}}$ = each disease, and ${\mathrm{s}}_{\mathrm{j}}$ = symptoms [11,30].

The Equation (14) is called max–min composition and calculates the membership function after the interaction of $\mathrm{Q}(\mathrm{P}⟶\mathrm{S})$ which links patients with symptoms, and $\mathrm{R}(\mathrm{S}⟶\mathrm{D})$ which links symptoms with disease [4,10,11].

The non-membership function we used was the $\propto$-composite fuzzy relation. Let $\mathrm{Q}(\mathrm{P}⟶\mathrm{S})$ and $\mathrm{R}(\mathrm{S}⟶\mathrm{D})$ be two fuzzy relations. We defined $\mathrm{T}=\mathrm{R}\propto \mathrm{Q}$ and $\mathrm{T}\in \left(\mathrm{P}\times \mathrm{D}\right)$ by $\left(\mathrm{R}\propto \mathrm{Q}\right)\left(\mathrm{p},\mathrm{d}\right)={\bigwedge }_{\mathrm{s}}[\mathrm{Q}\left(\mathrm{p},\mathrm{s}\right)\propto \mathrm{R}(\mathrm{s},\mathrm{d}\left)\right]$ or

$${\mathsf{\nu }}_{\mathrm{T}}\left({\mathrm{p}}_{\mathrm{l}},{\mathrm{d}}_{\mathrm{m}}\right)=\underset{\mathrm{s}\in \mathrm{S}}{\bigwedge }\left[{\mathsf{\nu }}_{\mathrm{Q}}\right({\mathrm{p}}_l,{\mathrm{s}}_{\mathrm{j}}\left)\mathrm{\bigvee }{\mathsf{\nu }}_{\mathrm{R}}\right({\mathrm{s}}_{\mathrm{j}},{\mathrm{d}}_{\mathrm{m}}\left)\right]$$

(15)

where $\mathrm{s}\in \mathrm{S},$ for all $(\mathrm{p},\mathrm{d})\in \mathrm{P}\times \mathrm{D}$, $\mathrm{\bigvee }=\mathrm{m}\mathrm{a}\mathrm{x}$ and $\mathrm{\bigwedge }=\mathrm{m}\mathrm{i}\mathrm{n}$, ${\mathrm{p}}_{\mathrm{l}}$ = patient for $l=1\dots \mathrm{L}$, ${\mathrm{d}}_{\mathrm{m}}$ = each disease, and ${\mathrm{s}}_{\mathrm{j}}$ = symptoms [11,30].

The Equation (15) is called min–max composition and calculates the non-membership function after the interaction of $\mathrm{Q}(\mathrm{P}⟶\mathrm{S})$ which links patients with symptoms, and $\mathrm{R}(\mathrm{S}⟶\mathrm{D})$ which links symptoms with disease [4,10,11].

Composite Fuzzy Relation 2 (CFR2)

There is another way to calculate the composition between two fuzzy relations. Let $\mathrm{Q}(\mathrm{P}⟶\mathrm{S})$ and $\mathrm{R}(\mathrm{S}⟶\mathrm{D})$ be two fuzzy relations. We defined $\mathrm{T}=\mathrm{R}\circ \mathrm{Q}$, $\mathrm{T}\in \left(\mathrm{P}\times \mathrm{D}\right),$ and the max-average composition of $\mathrm{R}$ and $\mathrm{Q}$ by the membership function:

$${\mathsf{\mu }}_{\mathrm{T}}\left({\mathrm{p}}_l,{\mathrm{d}}_{\mathrm{m}}\right)=\underset{\mathrm{s}\in \mathrm{S}}{\bigvee }\left[\frac{{\mathsf{\mu }}_{\mathrm{Q}}\left({\mathrm{p}}_l,{\mathrm{s}}_{\mathrm{j}}\right)+{\mathsf{\mu }}_{\mathrm{R}}({\mathrm{s}}_{\mathrm{j}},{\mathrm{d}}_{\mathrm{m}})}{2}\right]$$

(16)

where $\mathrm{s}\in \mathrm{S},$ for all $(\mathrm{p},\mathrm{d})\in \mathrm{P}\times \mathrm{D}$, $\mathrm{\bigvee }=\mathrm{m}\mathrm{a}\mathrm{x}$, ${\mathrm{p}}_{\mathrm{l}}$ = patient for $\mathrm{l}=1\dots \mathrm{L}$, ${\mathrm{d}}_{\mathrm{m}}$ = each disease, and ${\mathrm{s}}_{\mathrm{j}}$ = symptoms [5].

For non-membership functions we used the min-average composition of $\mathrm{R}$ and $\mathrm{Q}$:

$${\mathsf{\nu }}_{\mathrm{T}}\left({\mathrm{p}}_l,{\mathrm{d}}_{\mathrm{m}}\right)=\underset{\mathrm{s}\in \mathrm{S}}{\bigwedge }\left[\frac{{\mathsf{\mu }}_{\mathrm{Q}}\left({\mathrm{p}}_l,{\mathrm{s}}_{\mathrm{j}}\right)+{\mathsf{\mu }}_{\mathrm{R}}({\mathrm{s}}_{\mathrm{j}},{\mathrm{d}}_{\mathrm{m}})}{2}\right]$$

(17)

where $\mathrm{s}\in \mathrm{S},$ for all $(\mathrm{p},\mathrm{d})\in \mathrm{P}\times \mathrm{D}$, $\mathrm{\bigwedge }=\mathrm{m}\mathrm{i}\mathrm{n}$, ${\mathrm{p}}_{\mathrm{l}}$ = patient for $l=1\dots \mathrm{L}$, ${\mathrm{d}}_{\mathrm{m}}$ = each disease, and ${\mathrm{s}}_{\mathrm{j}}$ = symptoms [5].

2.7. Relation Value

After the interaction between the $\mathrm{Q}$ relation and the $\mathrm{R}$ relation, we received the relation $\mathrm{T}(\mathrm{P}\to \mathrm{D})$, which linked patients with disease. The final decision was calculated from the equation of relation value (RV):

$${\mathrm{R}\mathrm{V}}_1=\mathsf{\mu }-\mathsf{\nu }\times \mathsf{\pi }$$

(18)

in which relationship we removed the uncertain factors of $\mathsf{\nu }$ and $\mathsf{\pi }$ from the degree of membership $\mathsf{\mu }$ and−1 ≤ RV_1 ≤ 1 [11,29]. There is also another equation that computes the relation value including the above parameters and the logarithm with base 2:

$${\mathrm{R}\mathrm{V}}_2=\mathsf{\mu }-\mathsf{\nu }-\mathsf{\pi }\times \frac{{\log }_2\left(1+\mathsf{\pi }\right)}{100}$$

(19)

where $-1\le {\mathrm{R}\mathrm{V}}_2\le 1$ [31]. The greater this relation value, the more likely the patient was to suffer from the disease.

2.8. Score and Accuracy Diagnosis of Patients

The score and accuracy are another way of deducing a result. Both concepts incorporate the degrees of membership and non-membership, and what the score is used for is to compare two q-ROFS. A patient suffers from a disease in which the score is the highest [32]. The functions:

$$\mathrm{S}\mathrm{c}={\mathsf{\mu }}^{\mathrm{q}}-{\mathsf{\nu }}^{\mathrm{q}}$$

(20)

$$\mathrm{A}\mathrm{c}\mathrm{c}={\mathsf{\mu }}^{\mathrm{q}}+{\mathsf{\nu }}^{\mathrm{q}}$$

(21)

are the score function (20) and the accuracy function (21), where $\mathsf{\mu }$ defines the degree of membership, $\mathsf{\nu }$ defines the degree of non-membership, and $\mathrm{q}$ is the q-rung of a q-ROF [4,32].

2.9. Similarity Measures

Similarity measures are another method in order to make a medical decision. These measures are new for medical diagnosis via extended fuzzy sets. The similarity is linked with a set of symptoms and diagnosis [33]. There are many types of similarity measures. We applied the cosine similarity (CS) [22], the similarity measure (S10) proposed by Peng [34], and the q-rung orthopair fuzzy cosine (q-ROFC) measure [35],

$$\mathrm{C}\mathrm{S}(\mathrm{A},\mathrm{B})=\frac{1}{\mathrm{n}}\sum _{\mathrm{i}=1}^{\mathrm{n}}\frac{{\mathsf{\mu }}_{\mathrm{A}}\left({\mathrm{x}}_{\mathrm{i}}\right)\times {\mathsf{\mu }}_{\mathrm{B}}\left({\mathrm{x}}_{\mathrm{i}}\right)+{\mathsf{\nu }}_{\mathrm{A}}\left({\mathrm{x}}_{\mathrm{i}}\right)\times {\mathsf{\nu }}_{\mathrm{B}}\left({\mathrm{x}}_{\mathrm{i}}\right)}{\sqrt{{{\mathsf{\mu }}_{\mathsf{A}}}^2\left(\mathrm{x}\right)+{{\mathsf{\nu }}_{\mathsf{A}}}^2\left(\mathrm{x}\right)}\times \sqrt{{{\mathsf{\mu }}_{\mathsf{{\rm B}}}}^2\left(\mathrm{x}\right)+{{\mathsf{\nu }}_{\mathsf{{\rm B}}}}^2\left(\mathrm{x}\right)}}$$

(22)

$$\mathrm{S}10(\mathrm{A},\mathrm{B})=\frac{1}{\mathrm{n}}\sum _{\mathrm{i}=1}^{\mathrm{n}}\frac{{{\mathsf{\mu }}_{\mathsf{A}}}^2\left(\mathrm{x}\right)\mathrm{\bigwedge }{{\mathsf{\mu }}_{\mathsf{{\rm B}}}}^2\left(\mathrm{x}\right)+(1-{{\mathsf{\nu }}_{\mathsf{A}}}^2\left(\mathrm{x}\right))\mathrm{\bigwedge }(1-{{\mathsf{\nu }}_{\mathsf{{\rm B}}}}^2\left(\mathrm{x}\right))}{{{\mathsf{\mu }}_{\mathsf{A}}}^2\left(\mathrm{x}\right)\mathrm{\bigvee }{{\mathsf{\mu }}_{\mathsf{{\rm B}}}}^2\left(\mathrm{x}\right)+(1-{{\mathsf{\nu }}_{\mathsf{A}}}^2\left(\mathrm{x}\right))\mathrm{\bigvee }(1-{{\mathsf{\nu }}_{\mathsf{{\rm B}}}}^2\left(\mathrm{x}\right))}$$

(23)

$$\begin{array}{c}\mathrm{q}-\mathrm{R}\mathrm{O}\mathrm{F}\mathrm{C}\left(\mathrm{A},\mathrm{B}\right)=\\ \frac{1}{\mathrm{n}}{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}}\frac{{{\mathsf{\mu }}_{\mathrm{A}}}^{\mathrm{q}}\left({\mathrm{x}}_{\mathrm{i}}\right)\times {{\mathsf{\mu }}_{\mathrm{B}}}^{\mathrm{q}}\left({\mathrm{x}}_{\mathrm{i}}\right)+{{\mathsf{\nu }}_{\mathrm{A}}}^{\mathrm{q}}\left({\mathrm{x}}_{\mathrm{i}}\right)\times {{\mathsf{\nu }}_{\mathrm{B}}}^{\mathrm{q}}\left({\mathrm{x}}_{\mathrm{i}}\right)+{{\mathsf{\pi }}_{\mathrm{A}}}^{\mathrm{q}}\left({\mathrm{x}}_{\mathrm{i}}\right)\times {{\mathsf{\pi }}_{\mathrm{B}}}^{\mathrm{q}}\left({\mathrm{x}}_{\mathrm{i}}\right)}{\sqrt{{{{\mathsf{\mu }}_{\mathsf{A}}}^2\left(\mathrm{x}\right)}^{\mathrm{q}}+{{{\mathsf{\nu }}_{\mathsf{A}}}^2\left(\mathrm{x}\right)}^{\mathrm{q}}+{{{\mathsf{\pi }}_{\mathsf{A}}}^2\left(\mathrm{x}\right)}^{\mathrm{q}}}\times \sqrt{{{{\mathsf{\mu }}_{\mathsf{{\rm B}}}}^2\left(\mathrm{x}\right)}^{\mathrm{q}}+{{{\mathsf{\nu }}_{\mathsf{{\rm B}}}}^2\left(\mathrm{x}\right)}^{\mathrm{q}}+{{{\mathsf{\pi }}_{\mathsf{A}}}^2\left(\mathrm{x}\right)}^{\mathrm{q}}}}\end{array}$$

(24)

where $\mathrm{n}$ is the total number of items for each fuzzy set, and $\mathrm{q}$ is the $\mathrm{q}$ rung.

In order to find a proper diagnosis, we calculated for each patient ${\mathrm{p}}_{\mathrm{l}}$ where $\mathrm{l}\in \left\{1,\dots ,\mathrm{L}\right\}$, the similarity measures (22,23,24) for CS, S10, q-ROFC $\left(\mathrm{S}\left({\mathrm{p}}_{\mathrm{l}}\right),{\mathrm{d}}_{\mathrm{m}}\right)$ between patient symptoms, and the set of symptoms that are characteristic for each diagnosis ${\mathrm{d}}_{\mathrm{m}}$, where $\mathrm{m}\in \left\{1,\dots ,\mathrm{M}\right\}$. Our aim was to classify each patient with symptom $\mathrm{S}=\left\{{\mathrm{s}}_1,{\mathrm{s}}_2,\dots ,{\mathrm{s}}_{\mathrm{n}}\right\}$ in a disease ${\mathrm{d}}_{\mathrm{m}}$. The proper diagnosis ${\mathrm{d}}_{{\mathrm{m}}^{\mathrm{*}}}$ [36] of lth patient ${\mathrm{p}}_{\mathrm{l}}$ was derived according to:

$${\mathrm{m}}^{\mathrm{*}}=\mathrm{a}\mathrm{r}\mathrm{g}\underset{1\le \mathrm{m}\le \mathrm{M}}{\max }\left[\mathrm{Similarity}\mathrm{measure}\left(\mathrm{S}\left({\mathrm{p}}_l\right),{\mathrm{d}}_{\mathrm{m}}\right)\right]$$

(25)

where $\mathrm{S}\left({\mathrm{p}}_{\mathrm{l}}\right)=\left\{〈{\mathrm{s}}_{\mathrm{j}},{\mathsf{\mu }}_{{\mathrm{p}}_l}\left({\mathrm{s}}_{\mathrm{j}}\right),{\mathsf{\nu }}_{{\mathrm{p}}_l}\left({\mathrm{s}}_{\mathrm{j}}\right)〉|{\mathrm{s}}_{\mathrm{j}}\in \mathrm{S}\right\},\mathrm{j}=\mathrm{1,2},\dots ,\mathrm{n}$.

Therefore, it was identified with the lth patient, the diagnosis whose symptoms have the largest similarity measure to the patient’s symptoms.

2.10. Medical Data

There are five diseases $(\mathrm{M}=5)$ D = {viral fever, malaria fever, typhoid fever, stomach problems, and chest problems} and five symptoms $(\mathrm{n}=5)$ on the universe of discourse S = {temperature, headache, stomach pain, cough, and chest pain}.

Table 1. Medical knowledge R.

Symptoms\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problem	Chest Problem
temperature	〈0.4 0.0〉	〈0.7 0.0〉	〈0.3 0.3〉	〈0.1 0.7〉	〈0.1 0.8〉
headache	〈0.3 0.5〉	〈0.2 0.6〉	〈0.6 0.1〉	〈0.2 0.4〉	〈0.0 0.8〉
stomach pain	〈0.1 0.7〉	〈0.0 0.9〉	〈0.2 0.7〉	〈0.8 0.0〉	〈0.2 0.8〉
cough	〈0.4 0.3〉	〈0.7 0.0〉	〈0.2 0.6〉	〈0.2 0.7〉	〈0.2 0.8〉
chest pain	〈0.1 0.7〉	〈0.1 0.8〉	〈0.1 0.9〉	〈0.2 0.7〉	〈0.8 0.1〉

and

Table 2. Patient’s Symptoms Q (hypothetically the medical examination).

Patient\Symptoms	Temperature	Headache	Stomach Pain	Cough	Chest Pain
${\mathrm{p}}_1$	〈0.8 0.1〉	〈0.6 0.1〉	〈0.2 0.8〉	〈0.6 0.1〉	〈0.1 0.6〉
${\mathrm{p}}_2$	〈0.0 0.8〉	〈0.4 0.4〉	〈0.6 0.1〉	〈0.1 0.7〉	〈0.1 0.8〉
${\mathrm{p}}_3$	〈0.8 0.1〉	〈0.8 0.1〉	〈0.0 0.6〉	〈0.2 0.7〉	〈0.0 0.5〉
${\mathrm{p}}_4$	〈0.6 0.1〉	〈0.5 0.4〉	〈0.3 0.4〉	〈0.7 0.2〉	〈0.3 0.4〉

use data from [4,5,10,11,17,18,23]. The first number indicates the degree of membership, and the second number indicates the degree of non-membership. For example, in Table 1, cough had a 0.2 degree of membership and a 0.6 degree of non-membership for typhoid fever. In Table 2, P₂ had a 0.6 degree of membership and a 0.1 degree of non-membership in stomach pain. The medical knowledge $\mathrm{R}$ linked the symptoms with the disease, and this knowledge is represented in the following table:

There were four patients $(\mathrm{L}=4)$, that is, ${\mathrm{p}}_1,{\mathrm{p}}_2,{\mathrm{p}}_3,{\mathrm{p}}_4$ from whom medical data have been received. The patient’s symptoms, $\mathrm{Q}$, link each patient to symptoms. Data were obtained from patients twice. In order to precisely diagnose the patient’s disease, the doctor may have had more than one opinion. The doctor not only consulted the medical examination results but also consulted the patient’s history and how he/she felt [37]. The fusion of these aspects was carried out with aggregation operators so that a more realistic result was achieved due to containing more than one expert’s opinion.

The following were modified in relation to the data in Table 2. The modification was made at random and showed that the second opinion of the doctor was different from the first opinion. Suppose that Table 2 is the medical examination, the doctor’s opinion depended on the measurement carried out by the diagnosis and

Table 3. Patient’s Symptoms Q (hypothetically the patient’s history).

Patient\Symptoms	Temperature	Headache	Stomach Pain	Cough	Chest Pain
${\mathrm{p}}_1$	〈0.9 0.0〉	〈0.5 0.0〉	〈0.2 0.7〉	〈0.7 0.0〉	〈0.1 0.5〉
${\mathrm{p}}_2$	〈0.0 0.8〉	〈0.5 0.4〉	〈0.7 0.0〉	〈0.1 0.7〉	〈0.0 0.7〉
${\mathrm{p}}_3$	〈0.7 0.1〉	〈0.8 0.1〉	〈0.0 0.7〉	〈0.3 0.6〉	〈0.0 0.5〉
${\mathrm{p}}_4$	〈0.7 0.0〉	〈0.5 0.3〉	〈0.4 0.5〉	〈0.7 0.1〉	〈0.2 0.4〉

refers to the auxiliary medical information supplied by the patient.

2.11. Aggregation Operators

Aggregation operators are the special functions used to combine information or opinions in systems, where several sources of information must be taken into account to achieve a goal [38]. There are many operators for information fusion, but, in this paper, aggregation operators in [39,40] were used, as well as the arithmetic mean and harmonic mean. The aim was to combine the data from the medical examination (Table 2) with the data from the patient’s history (Table 3). The ${\mathrm{r}}_{\mathrm{i}}$ indicated the item involved in the fusion. Some of the following operators had the significance ${\mathrm{u}}_{\mathrm{i}}$. Τhus, by placing significance on the data we wanted to combine, we showed which aspect was more dominant. In this paper, was used ${\mathrm{u}}_1=0.6$ for the medical examination (Table 2) and ${\mathrm{u}}_2=0.4$ for the patient’s history (Table 3).

• Arithmetic Mean

$$\mathrm{M}({\mathrm{r}}_1,{\mathrm{r}}_2,\dots {\mathrm{r}}_{\mathrm{n}})=\frac{{\sum }_{\mathrm{i}}^{\mathrm{n}}{\mathrm{r}}_{\mathrm{i}}}{\mathrm{n}}$$

(26)

where ${\mathrm{r}}_{\mathrm{i}}$ is the value and $\mathrm{n}$ is the total number of ${\mathrm{r}}_{\mathrm{i}}$.

• Harmonic Mean

$$\mathrm{H}\left({\mathrm{r}}_1,{\mathrm{r}}_2,\dots {\mathrm{r}}_{\mathrm{n}}\right)=\frac{\mathrm{n}}{\frac{1}{{\mathrm{r}}_1}+\frac{1}{{\mathrm{r}}_2}+\dots +\frac{1}{{\mathrm{r}}_{\mathrm{n}}}}$$

(27)

where ${\mathrm{r}}_{\mathrm{i}}$ is the value and $\mathrm{n}$ is the total number of ${\mathrm{r}}_{\mathrm{i}}$.

• Bellaman-Zadeh [39]

$$\mathrm{A}\mathrm{g}\mathrm{g}\left[\left({\mathrm{r}}_1,{\mathrm{r}}_2,\dots {\mathrm{r}}_{\mathrm{n}}\right)\right]={\mathrm{M}\mathrm{i}\mathrm{n}}_{\mathrm{i}}\left[{\mathrm{r}}_{\mathrm{i}}\right]$$

(28)

where ${\mathrm{r}}_{\mathrm{i}}$ is the value and $\mathrm{n}$ is the total number of ${\mathrm{r}}_{\mathrm{i}}$.

• I-Ordered weighted average (I-OWA) [39]

Using the linguistic quantifier $\mathrm{Q}$ as the unitor quantifier: $\mathrm{Q}\left(\mathsf{\rho }\right)=\mathsf{\rho }$, the weights ${\mathsf{\omega }}_{\mathrm{n}}$ were calculated by: ${\mathsf{\omega }}_{\mathrm{n}}\left(\mathrm{x}\right)=\mathrm{Q}\left(\frac{\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{u}}_{\mathrm{i}}}{\mathrm{T}}\right)-\mathrm{Q}\left(\frac{\sum _{\mathrm{i}=1}^{\mathrm{n}-1}{\mathrm{u}}_{\mathrm{i}}}{\mathrm{T}}\right)\stackrel{\mathrm{Q}\left(\mathrm{b}\right)=\mathrm{b}}{\to }{\mathsf{\omega }}_{\mathrm{n}}\left(\mathrm{x}\right)=\frac{\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{u}}_{\mathrm{i}}}{\mathrm{T}}-\frac{\sum _{\mathrm{i}=1}^{\mathrm{n}-1}{\mathrm{u}}_{\mathrm{i}}}{\mathrm{T}}=\frac{{\mathrm{u}}_{\mathrm{n}}}{\mathrm{T}}$, where $\mathrm{T}=\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{u}}_{\mathrm{i}}$, ${\mathrm{u}}_{\mathrm{i}}$ is importance and $\mathrm{n}$ is the total number of ${\mathrm{u}}_{\mathrm{i}}$. So, the OWA aggregation using these weights is:

$$\mathrm{I}-\mathrm{O}\mathrm{W}\mathrm{A}({\mathrm{r}}_1,{\mathrm{r}}_2,\dots {\mathrm{r}}_{\mathrm{n}})=\frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{u}}_{\mathrm{i}}{\mathrm{r}}_{\mathrm{i}}}{\mathrm{T}}$$

(29)

where ${\mathrm{u}}_{\mathrm{i}}$ is the importance of ${\mathrm{r}}_{\mathrm{i}}$, $\mathrm{T}=\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{u}}_{\mathrm{i}}$, ${\mathrm{r}}_{\mathrm{i}}$ is the value item, and $\mathrm{n}$ is the total number of value items.

• q-Rung Orthopair Fuzzy weighted averaging operator (q-ROFWA) [40]. Suppose ${\mathbf{r}}_{\mathbf{k}}=$〈${\mathsf{\mu }}_{\mathbf{k}},{\mathsf{\nu }}_{\mathbf{k}}\rangle \left(\mathbf{k}=1,2,\dots ,\mathbf{n}\right)$ is a collection of q-ROF numbers. The aggregation result is:

$$\mathrm{q}-\mathrm{R}\mathrm{O}\mathrm{F}\mathrm{W}\mathrm{A}({\mathrm{r}}_1,{\mathrm{r}}_2,\dots {\mathrm{r}}_{\mathrm{n}})=\langle {\left(1-\prod _{\mathrm{i}=1}^{\mathrm{n}}{\left(1-{\mathsf{\mu }}_{\mathrm{i}}^{\mathrm{q}}\right)}^{{\mathrm{u}}_{\mathrm{i}}}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{q}$}\right.},\prod _{\mathrm{i}=1}^{\mathrm{n}}{\mathsf{\nu }}_{\mathrm{i}}^{{\mathrm{u}}_{\mathrm{i}}}\rangle$$

(30)

where ${\mathsf{\mu }}_{\mathrm{i}}$ is the degree of membership, ${\mathsf{\nu }}_{\mathrm{i}}$ is the degree of non-membership, $\mathrm{q}$ is the $\mathrm{q}$th rung, and $\mathrm{n}$ is the total number of ${\mathrm{r}}_{\mathrm{k}}$.

2.12. Employed Algorithm

The algorithm that simulated the medical problem and the steps to consider the medical decision were as follows:

Step 1: Provided a set of patients P, a set of diseases D, and a set of symptoms S.

Step 2: Established the medical knowledge R. This knowledge linked the symptoms to the diseases R(S→D).

Step 3: Choosing a method for decision-making. If there was patient history, aFggregation operators and Sanchez’s formula were recommended. Otherwise, composite fuzzy relations or similarity measures were suggested. The methods were:

1.

Composite Fuzzy Relation:

1.1

Establishing the patients’ symptoms Q. This relation linked the patients to the symptoms Q(P→S).

1.2

Choosing between CFR1 and CFR2. Using max-min and min-max compositions, degrees of membership and non-membership were calculated.

1.3

Using relation value (RV1 or RV2) or score and accuracy, the final result was calculated.

2.

Aggregation operators and q-ROFS:

2.1

In this option, the patient’s history was recommended.

2.2

Choosing the q rung. The extended fuzzy sets, q-ROFs, required a value in q, where $\mathbf{q}\ge 1.$

2.3

Using an aggregation method based on aggregation operators. In this step, the two aspects of the medical specialists were fused into one. Thus, a new Q comes out (Q’). The relation Q’ linked the patients to the symptoms Q’(P→S).

2.4

Using the Sanchez’s method (CFR1). Using max-min and min-max compositions, degrees of membership and non-membership were calculated.

2.5

Using relation value (RV1 or RV2), or score and accuracy, the final result was calculated.

3.

Similarity measures:

3.1

Establishing the patients’ symptoms Q. This relation links the patients to the symptoms Q(P→S).

3.2

Choosing the cosine, Peng, or q-ROFC similarity measure, to calculate the final result.

Step 4: The final disease corresponded to the maximum value for each patient, for every disease. If the results were not acceptable, the medical knowledge R was modified, and the algorithm was run again.

3. Results

3.1. Composite Fuzzy Relation

A medical diagnosis was made through composite fuzzy relations. Applying Equations (14) and (15) for composite fuzzy relation 1 and Equations (16) and (17) for composite fuzzy relation 2, in Table 1 and Table 2, a table of membership and non-membership degrees is detailed. By using relation value (Equation (18) or Equation (19)) or score and accuracy (Equations (20) and (21)), the final table of decision was calculated. Table 4, Table 5, Table 6 and Table 7 show the results using composite fuzzy relation 1 and Table 8, Table 9, Table 10 and Table 11 show the results using composite fuzzy relation 2.

Composite Fuzzy Relation 1

Table 4. Membership and Non-membership degrees.

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.6〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.4, 0.4〉	〈0.6, 0.1〉	〈0.2, 0.8〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.5, 0.3〉	〈0.3, 0.4〉	〈0.3, 0.4〉

Table 4. Membership and Non-membership degrees.

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.6〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.4, 0.4〉	〈0.6, 0.1〉	〈0.2, 0.8〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.5, 0.3〉	〈0.3, 0.4〉	〈0.3, 0.4〉

Table 5. Final decision with ${\mathrm{R}\mathrm{V}}_1.$

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3500	0.6800	0.5700	0.0400	0.0800
P2	0.2000	0.0800	0.3200	0.5700	0.2000
P3	0.3500	0.6800	0.5700	0.0400	0.0500
P4	0.3500	0.6800	0.4400	0.1800	0.1800

Patient P₁ suffered from malaria fever with relation value (0.6800); patient P₂ suffered from stomach problems with relation value (0.5700); patient P₃ suffered from malaria fever with relation value (0.6800); patient P₄ suffered from malaria fever with relation value (0.6800).

Table 5. Final decision with ${\mathrm{R}\mathrm{V}}_1.$

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3500	0.6800	0.5700	0.0400	0.0800
P2	0.2000	0.0800	0.3200	0.5700	0.2000
P3	0.3500	0.6800	0.5700	0.0400	0.0500
P4	0.3500	0.6800	0.4400	0.1800	0.1800

Patient P₁ suffered from malaria fever with relation value (0.6800); patient P₂ suffered from stomach problems with relation value (0.5700); patient P₃ suffered from malaria fever with relation value (0.6800); patient P₄ suffered from malaria fever with relation value (0.6800).

Table 6. Final decision with ${\mathrm{R}\mathrm{V}}_2.$

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.2971	0.5995	0.4989	−0.2019	−0.4005
P2	−0.2005	−0.4005	−0.0005	0.4989	−0.6000
P3	0.2971	0.5995	0.4989	−0.2019	−0.3011
P4	0.2971	0.5995	0.1995	−0.1011	−0.1011

Patient P₁ suffered from malaria fever with relation value (0.5995); patient P₂ suffered from stomach problems with relation value (0.4989); patient P₃ suffered from malaria fever with relation value (0.5995); patient P₄ suffered from malaria fever with relation value (0.5995).

Table 6. Final decision with ${\mathrm{R}\mathrm{V}}_2.$

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.2971	0.5995	0.4989	−0.2019	−0.4005
P2	−0.2005	−0.4005	−0.0005	0.4989	−0.6000
P3	0.2971	0.5995	0.4989	−0.2019	−0.3011
P4	0.2971	0.5995	0.1995	−0.1011	−0.1011

Patient P₁ suffered from malaria fever with relation value (0.5995); patient P₂ suffered from stomach problems with relation value (0.4989); patient P₃ suffered from malaria fever with relation value (0.5995); patient P₄ suffered from malaria fever with relation value (0.5995).

Table 7. Score and Accuracy.

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.3, 0.5〉	〈0.6, 0.8〉	〈0.5, 0.7〉	〈−0.2, 0.6〉	〈−0.4, 0.8〉
P2	〈−0.2, 0.8〉	〈−0.4, 0.8〉	〈0.0, 0.8〉	〈0.5, 0.7〉	〈−0.6, 1.0〉
P3	〈0.3, 0.5〉	〈0.6, 0.8〉	〈0.5, 0.7〉	〈−0.2, 0.6〉	〈−0.3, 0.7〉
P4	〈0.3, 0.5〉	〈0.6, 0.8〉	〈0.2, 0.8〉	〈−0.1, 0.7〉	〈−0.1, 0.7〉

Patient P₁ suffered from malaria fever with score (0.6); patient P₂ suffered from stomach problems with score (0.5); patient P₃ suffered from malaria fever with score (0.6); patient P₄ suffered from malaria fever with score (0.6).

Table 7. Score and Accuracy.

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.3, 0.5〉	〈0.6, 0.8〉	〈0.5, 0.7〉	〈−0.2, 0.6〉	〈−0.4, 0.8〉
P2	〈−0.2, 0.8〉	〈−0.4, 0.8〉	〈0.0, 0.8〉	〈0.5, 0.7〉	〈−0.6, 1.0〉
P3	〈0.3, 0.5〉	〈0.6, 0.8〉	〈0.5, 0.7〉	〈−0.2, 0.6〉	〈−0.3, 0.7〉
P4	〈0.3, 0.5〉	〈0.6, 0.8〉	〈0.2, 0.8〉	〈−0.1, 0.7〉	〈−0.1, 0.7〉

Patient P₁ suffered from malaria fever with score (0.6); patient P₂ suffered from stomach problems with score (0.5); patient P₃ suffered from malaria fever with score (0.6); patient P₄ suffered from malaria fever with score (0.6).

Composite Fuzzy Relation 2

Table 8. Membership and Non-membership degrees.

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.6, 0.05〉	〈0.65, 0.05〉	〈0.25, 0.55〉	〈0.35, 0.4〉	〈0.1, 0.7〉
P2	〈0.15, 0.65〉	〈0.3, 0.5〉	〈0.6, 0.1〉	〈0.15, 0.55〉	〈0.05, 0.8〉
P3	〈0.45, 0.4〉	〈0.4, 0.5〉	〈0.1, 0.65〉	〈0.5, 0.35〉	〈0.1, 0.65〉
P4	〈0.5, 0.2〉	〈0.6, 0.2〉	〈0.25, 0.5〉	〈0.45, 0.45〉	〈0.25, 0.6〉

Table 8. Membership and Non-membership degrees.

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.6, 0.05〉	〈0.65, 0.05〉	〈0.25, 0.55〉	〈0.35, 0.4〉	〈0.1, 0.7〉
P2	〈0.15, 0.65〉	〈0.3, 0.5〉	〈0.6, 0.1〉	〈0.15, 0.55〉	〈0.05, 0.8〉
P3	〈0.45, 0.4〉	〈0.4, 0.5〉	〈0.1, 0.65〉	〈0.5, 0.35〉	〈0.1, 0.65〉
P4	〈0.5, 0.2〉	〈0.6, 0.2〉	〈0.25, 0.5〉	〈0.45, 0.45〉	〈0.25, 0.6〉

Table 9. Final decision with ${\mathrm{R}\mathrm{V}}_1.$

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.5825	0.6350	0.1400	0.2500	−0.0400
P2	0.0200	0.2000	0.5700	−0.0150	−0.0700
P3	0.3900	0.3500	−0.0625	0.4475	−0.0625
P4	0.4400	0.5600	0.1250	0.4050	0.1600

Patient P₁ suffered from malaria fever with relation value (0.6350); patient P₂ suffered from typhoid fever with relation value (0.5700); patient P₃ suffered from stomach problems with relation value (0.4475); patient P₄ suffered from malaria fever with relation value (0.5600).

Table 9. Final decision with ${\mathrm{R}\mathrm{V}}_1.$

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.5825	0.6350	0.1400	0.2500	−0.0400
P2	0.0200	0.2000	0.5700	−0.0150	−0.0700
P3	0.3900	0.3500	−0.0625	0.4475	−0.0625
P4	0.4400	0.5600	0.1250	0.4050	0.1600

Patient P₁ suffered from malaria fever with relation value (0.6350); patient P₂ suffered from typhoid fever with relation value (0.5700); patient P₃ suffered from stomach problems with relation value (0.4475); patient P₄ suffered from malaria fever with relation value (0.5600).

Table 10. Final decision with ${\mathrm{R}\mathrm{V}}_2.$

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.5485	0.5989	−0.3005	−0.0508	−0.6005
P2	−0.5005	−0.2005	0.4989	−0.4011	−0.7503
P3	0.0497	−0.1001	−0.5508	0.1497	−0.5508
P4	0.2989	0.3995	−0.2508	−0.0001	−0.3503

Patient P₁ suffered from malaria fever with relation value (0.5485); patient P₂ suffered from typhoid fever with relation value (0.4989); patient P₃ suffered from stomach problems with relation value (0.1497); patient P₄ suffered from malaria fever with relation value (0.3995).

Table 10. Final decision with ${\mathrm{R}\mathrm{V}}_2.$

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.5485	0.5989	−0.3005	−0.0508	−0.6005
P2	−0.5005	−0.2005	0.4989	−0.4011	−0.7503
P3	0.0497	−0.1001	−0.5508	0.1497	−0.5508
P4	0.2989	0.3995	−0.2508	−0.0001	−0.3503

Patient P₁ suffered from malaria fever with relation value (0.5485); patient P₂ suffered from typhoid fever with relation value (0.4989); patient P₃ suffered from stomach problems with relation value (0.1497); patient P₄ suffered from malaria fever with relation value (0.3995).

Table 11. Score and Accuracy.

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.55, 0.65〉	〈0.6, 0.7〉	〈−0.3, 0.8〉	〈−0.05, 0.75〉	〈−0.6, 0.8〉
P2	〈−0.5, 0.8〉	〈−0.2, 0.8〉	〈0.5, 0.7〉	〈−0.4, 0.7〉	〈−0.75, 0.85〉
P3	〈0.05, 0.85〉	〈−0.1, 0.9〉	〈−0.55, 0.75〉	〈0.15, 0.85〉	〈−0.55, 0.75〉
P4	〈0.3, 0.7〉	〈0.4, 0.8〉	〈−0.25, 0.75〉	〈0.0, 0.9〉	〈−0.35, 0.85〉

Patient P₁ suffered from malaria fever with score (0.6); patient P₂ suffered from typhoid fever with score (0.5); patient P₃ suffered from stomach problems with score (0.15); patient P₄ suffered from malaria fever with score (0.4).

Table 11. Score and Accuracy.

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.55, 0.65〉	〈0.6, 0.7〉	〈−0.3, 0.8〉	〈−0.05, 0.75〉	〈−0.6, 0.8〉
P2	〈−0.5, 0.8〉	〈−0.2, 0.8〉	〈0.5, 0.7〉	〈−0.4, 0.7〉	〈−0.75, 0.85〉
P3	〈0.05, 0.85〉	〈−0.1, 0.9〉	〈−0.55, 0.75〉	〈0.15, 0.85〉	〈−0.55, 0.75〉
P4	〈0.3, 0.7〉	〈0.4, 0.8〉	〈−0.25, 0.75〉	〈0.0, 0.9〉	〈−0.35, 0.85〉

Patient P₁ suffered from malaria fever with score (0.6); patient P₂ suffered from typhoid fever with score (0.5); patient P₃ suffered from stomach problems with score (0.15); patient P₄ suffered from malaria fever with score (0.4).

3.2. Aggregation Operators and q-ROFS

Aggregation operators combined multiple experts’ opinions. By applying these operators (Equations (26) and (30)) in Table 2 and Table 3, a final table of patient symptoms was obtained. According to Sanchez’s method, Equations (14) and (15) should be applied to calculate the table of membership and non-membership degrees. In addition, a value in q-rung is required because of q-ROFSs. By using relation value (Equation (18) or Equation (19)) or score and accuracy (Equations (20) and (21)), the final table of decision was calculated. Table 12, Table 13, Table 14, Table 15, Table 16, Table 17, Table 18, Table 19, Table 20, Table 21, Table 22, Table 23, Table 24, Table 25, Table 26, Table 27, Table 28, Table 29, Table 30 and Table 31 show the results using aggregation operators and intuitionistic fuzzy sets (q = 1). Table 32, Table 33, Table 34, Table 35, Table 36, Table 37, Table 38, Table 39, Table 40, Table 41, Table 42, Table 43, Table 44, Table 45, Table 46, Table 47, Table 48, Table 49, Table 50 and Table 51 show the results using aggregation operators and Pythagorean fuzzy sets (q = 2). Table 52, Table 53, Table 54, Table 55, Table 56, Table 57, Table 58, Table 59, Table 60, Table 61, Table 62, Table 63, Table 64, Table 65, Table 66, Table 67, Table 68, Table 69, Table 70 and Table 71 show the results using aggregation operators and Fermatean fuzzy sets (q = 3).

Intuitionistic Fuzzy Sets (q = 1)

Table 12. Membership and Non-membership degrees (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.05〉	〈0.7, 0.05〉	〈0.55, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.55〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.45, 0.4〉	〈0.65, 0.05〉	〈0.2, 0.75〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.05〉	〈0.7, 0.05〉	〈0.5, 0.3〉	〈0.35, 0.4〉	〈0.25, 0.4〉

Table 12. Membership and Non-membership degrees (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.05〉	〈0.7, 0.05〉	〈0.55, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.55〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.45, 0.4〉	〈0.65, 0.05〉	〈0.2, 0.75〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.05〉	〈0.7, 0.05〉	〈0.5, 0.3〉	〈0.35, 0.4〉	〈0.25, 0.4〉

Table 13. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3725	0.6875	0.5150	0.0400	0.0625
P2	0.2000	0.0800	0.3900	0.6350	0.1625
P3	0.3500	0.6800	0.5700	0.0400	0.0500
P4	0.3725	0.6875	0.4400	0.2500	0.1100

Patient P₁ suffered from malaria fever with relation value (0.6875); patient P₂ suffered from stomach problems with relation value (0.6350); patient P₃ suffers from malaria fever with relation value (0.6800); patient P₄ suffered from malaria fever with relation value (0.6875).

Table 13. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3725	0.6875	0.5150	0.0400	0.0625
P2	0.2000	0.0800	0.3900	0.6350	0.1625
P3	0.3500	0.6800	0.5700	0.0400	0.0500
P4	0.3725	0.6875	0.4400	0.2500	0.1100

Patient P₁ suffered from malaria fever with relation value (0.6875); patient P₂ suffered from stomach problems with relation value (0.6350); patient P₃ suffers from malaria fever with relation value (0.6800); patient P₄ suffered from malaria fever with relation value (0.6875).

Table 14. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3465	0.6492	0.4485	−0.2019	−0.3508
P2	−0.2005	−0.4005	0.0497	0.5989	−0.5500
P3	0.2971	0.5995	0.4989	−0.2019	−0.3011
P4	0.3465	0.6492	0.1995	−0.0508	−0.1515

Patient P₁ suffered from malaria fever with relation value (0.6492); patient P₂ suffered from stomach problems with relation value (0.5989); patient P₃ suffered from malaria fever with relation value (0.5995); patient P₄ suffered from malaria fever with relation value (0.6492).

Table 14. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3465	0.6492	0.4485	−0.2019	−0.3508
P2	−0.2005	−0.4005	0.0497	0.5989	−0.5500
P3	0.2971	0.5995	0.4989	−0.2019	−0.3011
P4	0.3465	0.6492	0.1995	−0.0508	−0.1515

Patient P₁ suffered from malaria fever with relation value (0.6492); patient P₂ suffered from stomach problems with relation value (0.5989); patient P₃ suffered from malaria fever with relation value (0.5995); patient P₄ suffered from malaria fever with relation value (0.6492).

Table 15. Score and Accuracy (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.35, 0.45〉	〈0.65, 0.75〉	〈0.45, 0.65〉	〈−0.2, 0.6〉	〈−0.35, 0.75〉
P2	〈−0.2, 0.8〉	〈−0.4, 0.8〉	〈0.05, 0.85〉	〈0.6, 0.7〉	〈−0.55, 0.95〉
P3	〈0.3, 0.5〉	〈0.6, 0.8〉	〈0.5, 0.7〉	〈−0.2, 0.6〉	〈−0.3, 0.7〉
P4	〈0.35, 0.45〉	〈0.65, 0.75〉	〈0.2, 0.8〉	〈−0.05, 0.75〉	〈−0.15, 0.65〉

Patient P₁ suffered from malaria fever with score (0.65); patient P₂ suffered from stomach problems with score (0.6); patient P₃ suffered from malaria fever with score (0.6); patient P₄ suffered from malaria fever with score (0.65).

Table 15. Score and Accuracy (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.35, 0.45〉	〈0.65, 0.75〉	〈0.45, 0.65〉	〈−0.2, 0.6〉	〈−0.35, 0.75〉
P2	〈−0.2, 0.8〉	〈−0.4, 0.8〉	〈0.05, 0.85〉	〈0.6, 0.7〉	〈−0.55, 0.95〉
P3	〈0.3, 0.5〉	〈0.6, 0.8〉	〈0.5, 0.7〉	〈−0.2, 0.6〉	〈−0.3, 0.7〉
P4	〈0.35, 0.45〉	〈0.65, 0.75〉	〈0.2, 0.8〉	〈−0.05, 0.75〉	〈−0.15, 0.65〉

Patient P₁ suffered from malaria fever with score (0.65); patient P₂ suffered from stomach problems with score (0.6); patient P₃ suffered from malaria fever with score (0.6); patient P₄ suffered from malaria fever with score (0.65).

Table 16. Membership and Non-membership degrees (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problem	Chest Problem
P1	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.54, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.54〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.44, 0.4〉	〈0.65, 0.0〉	〈0.2, 0.75〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.5, 0.3〉	〈0.34, 0.4〉	〈0.24, 0.4〉

Table 16. Membership and Non-membership degrees (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problem	Chest Problem
P1	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.54, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.54〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.44, 0.4〉	〈0.65, 0.0〉	〈0.2, 0.75〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.5, 0.3〉	〈0.34, 0.4〉	〈0.24, 0.4〉

Table 17. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.4000	0.7000	0.5100	0.0400	0.0612
P2	0.2000	0.0800	0.3822	0.6462	0.1602
P3	0.3500	0.6800	0.5700	0.0400	0.0500
P4	0.4000	0.7000	0.4400	0.2400	0.0960

Patient P₁ suffered from malaria fever with relation value (0.7000); patient P₂ suffered from stomach problems with relation value (0.6462); patient P₃ suffered from malaria fever with relation value (0.6800); patient P₄ suffered from malaria fever with relation value (0.7000).

Table 17. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.4000	0.7000	0.5100	0.0400	0.0612
P2	0.2000	0.0800	0.3822	0.6462	0.1602
P3	0.3500	0.6800	0.5700	0.0400	0.0500
P4	0.4000	0.7000	0.4400	0.2400	0.0960

Patient P₁ suffered from malaria fever with relation value (0.7000); patient P₂ suffered from stomach problems with relation value (0.6462); patient P₃ suffered from malaria fever with relation value (0.6800); patient P₄ suffered from malaria fever with relation value (0.7000).

Table 18. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3959	0.6989	0.4439	−0.2019	−0.3463
P2	−0.2005	−0.4005	0.0441	0.6646	−0.5467
P3	0.2971	0.5995	0.4989	−0.2019	−0.3011
P4	0.3959	0.6989	0.1995	−0.0580	−0.1616

Patient P₁ suffered from malaria fever with relation value (0.6989); patient P₂ suffered from stomach problems with relation value (0.6646); patient P₃ suffered from malaria fever with relation value (0.5995); patient P₄ suffered from malaria fever with relation value (0.6989).

Table 18. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3959	0.6989	0.4439	−0.2019	−0.3463
P2	−0.2005	−0.4005	0.0441	0.6646	−0.5467
P3	0.2971	0.5995	0.4989	−0.2019	−0.3011
P4	0.3959	0.6989	0.1995	−0.0580	−0.1616

Patient P₁ suffered from malaria fever with relation value (0.6989); patient P₂ suffered from stomach problems with relation value (0.6646); patient P₃ suffered from malaria fever with relation value (0.5995); patient P₄ suffered from malaria fever with relation value (0.6989).

Table 19. Score and Accuracy (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.4〉	〈0.7, 0.7〉	〈0.44, 0.64〉	〈−0.2, 0.6〉	〈−0.34, 0.74〉
P2	〈−0.2, 0.8〉	〈−0.4, 0.8〉	〈0.04, 0.84〉	〈0.65, 0.65〉	〈−0.55, 0.95〉
P3	〈0.3, 0.5〉	〈0.6, 0.8〉	〈0.5, 0.7〉	〈−0.2, 0.6〉	〈−0.3, 0.7〉
P4	〈0.4, 0.4〉	〈0.7, 0.7〉	〈0.2, 0.8〉	〈−0.06, 0.74〉	〈−0.16, 0.64〉

Patient P₁ suffered from malaria fever with score (0.7); patient P₂ suffered from stomach problems with score (0.65); patientP₃ suffered from malaria fever with score (0.6); patient P₄ suffered from malaria fever with score (0.7).

Table 19. Score and Accuracy (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.4〉	〈0.7, 0.7〉	〈0.44, 0.64〉	〈−0.2, 0.6〉	〈−0.34, 0.74〉
P2	〈−0.2, 0.8〉	〈−0.4, 0.8〉	〈0.04, 0.84〉	〈0.65, 0.65〉	〈−0.55, 0.95〉
P3	〈0.3, 0.5〉	〈0.6, 0.8〉	〈0.5, 0.7〉	〈−0.2, 0.6〉	〈−0.3, 0.7〉
P4	〈0.4, 0.4〉	〈0.7, 0.7〉	〈0.2, 0.8〉	〈−0.06, 0.74〉	〈−0.16, 0.64〉

Patient P₁ suffered from malaria fever with score (0.7); patient P₂ suffered from stomach problems with score (0.65); patientP₃ suffered from malaria fever with score (0.6); patient P₄ suffered from malaria fever with score (0.7).

Table 20. Membership and Non-membership degrees (Aggregation: Bellaman/Zadeh).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.5, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.4, 0.4〉	〈0.6, 0.0〉	〈0.2, 0.7〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.5, 0.3〉	〈0.3, 0.4〉	〈0.2, 0.4〉

Table 20. Membership and Non-membership degrees (Aggregation: Bellaman/Zadeh).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.5, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.4, 0.4〉	〈0.6, 0.0〉	〈0.2, 0.7〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.5, 0.3〉	〈0.3, 0.4〉	〈0.2, 0.4〉

Table 21. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: Bellaman/Zadeh).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.4000	0.7000	0.4600	0.0400	0.0500
P2	0.2000	0.0800	0.3200	0.6000	0.1300
P3	0.3500	0.6800	0.5700	0.0400	0.0500
P4	0.4000	0.7000	0.4400	0.1800	0.0400

Patient P₁ suffered from malaria fever with relation value (0.7000); patient P₂ suffered from stomach problems with relation value (0.6000; patient P₃ suffered from malaria fever with relation value (0.6800); patientP₄ suffered from malaria fever with relation value (0.7000).

Table 21. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: Bellaman/Zadeh).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.4000	0.7000	0.4600	0.0400	0.0500
P2	0.2000	0.0800	0.3200	0.6000	0.1300
P3	0.3500	0.6800	0.5700	0.0400	0.0500
P4	0.4000	0.7000	0.4400	0.1800	0.0400

Patient P₁ suffered from malaria fever with relation value (0.7000); patient P₂ suffered from stomach problems with relation value (0.6000; patient P₃ suffered from malaria fever with relation value (0.6800); patientP₄ suffered from malaria fever with relation value (0.7000).

Table 22. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: Bellaman/Zadeh).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3959	0.6989	0.3981	−0.2019	−0.3011
P2	−0.2005	−0.4005	−0.0005	0.5981	−0.5001
P3	0.2971	0.5995	0.4989	−0.2019	−0.3011
P4	0.3959	0.6989	0.1995	−0.1011	−0.2019

Patient P₁ suffered from malaria fever with relation value (0.6989); patientP₂ suffered from stomach problems with relation value (0.5981); patient P₃ suffered from malaria fever with relation value (0.5995); patient P₄ suffered from malaria fever with relation value (0.6989).

Table 22. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: Bellaman/Zadeh).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3959	0.6989	0.3981	−0.2019	−0.3011
P2	−0.2005	−0.4005	−0.0005	0.5981	−0.5001
P3	0.2971	0.5995	0.4989	−0.2019	−0.3011
P4	0.3959	0.6989	0.1995	−0.1011	−0.2019

Patient P₁ suffered from malaria fever with relation value (0.6989); patientP₂ suffered from stomach problems with relation value (0.5981); patient P₃ suffered from malaria fever with relation value (0.5995); patient P₄ suffered from malaria fever with relation value (0.6989).

Table 23. Score and Accuracy (Aggregation: Bellaman/Zadeh).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.4〉	〈0.7, 0.7〉	〈0.4, 0.6〉	〈−0.2, 0.6〉	〈−0.3, 0.7〉
P2	〈−0.2, 0.8〉	〈−0.4, 0.8〉	〈0.0, 0.8〉	〈0.6, 0.6〉	〈−0.5, 0.9〉
P3	〈0.3, 0.5〉	〈0.6, 0.8〉	〈0.5, 0.7〉	〈−0.2, 0.6〉	〈−0.3, 0.7〉
P4	〈0.4, 0.4〉	〈0.7, 0.7〉	〈0.2, 0.8〉	〈−0.1, 0.7〉	〈−0.2, 0.6〉

Patient P₁ suffered from malaria fever with score (0.7); patient P₂ suffered from stomach problems with score (0.6); patient P₃ suffered from malaria fever with score (0.6); patient P₄ suffered from malaria fever with score (0.7).

Table 23. Score and Accuracy (Aggregation: Bellaman/Zadeh).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.4〉	〈0.7, 0.7〉	〈0.4, 0.6〉	〈−0.2, 0.6〉	〈−0.3, 0.7〉
P2	〈−0.2, 0.8〉	〈−0.4, 0.8〉	〈0.0, 0.8〉	〈0.6, 0.6〉	〈−0.5, 0.9〉
P3	〈0.3, 0.5〉	〈0.6, 0.8〉	〈0.5, 0.7〉	〈−0.2, 0.6〉	〈−0.3, 0.7〉
P4	〈0.4, 0.4〉	〈0.7, 0.7〉	〈0.2, 0.8〉	〈−0.1, 0.7〉	〈−0.2, 0.6〉

Patient P₁ suffered from malaria fever with score (0.7); patient P₂ suffered from stomach problems with score (0.6); patient P₃ suffered from malaria fever with score (0.6); patient P₄ suffered from malaria fever with score (0.7).

Table 24. Membership and Non-membership degrees (Aggregation: I—OWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.06〉	〈0.7, 0.06〉	〈0.56, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.56〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.44, 0.4〉	〈0.64, 0.06〉	〈0.2, 0.76〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.06〉	〈0.7, 0.06〉	〈0.5, 0.3〉	〈0.34, 0.4〉	〈0.26, 0.4〉

Table 24. Membership and Non-membership degrees (Aggregation: I—OWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.06〉	〈0.7, 0.06〉	〈0.56, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.56〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.44, 0.4〉	〈0.64, 0.06〉	〈0.2, 0.76〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.06〉	〈0.7, 0.06〉	〈0.5, 0.3〉	〈0.34, 0.4〉	〈0.26, 0.4〉

Table 25. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: I—OWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problem	Chest Problem
P1	0.3676	0.6856	0.5260	0.0400	0.0656
P2	0.2000	0.0800	0.3760	0.6220	0.1696
P3	0.3500	0.6800	0.5700	0.0400	0.0500
P4	0.3676	0.6856	0.4400	0.2360	0.1240

Patient P₁ suffered from malaria fever with relation value (0.6856); patient P₂ suffered from stomach problems with relation value (0.6220); patient P₃ suffered from malaria fever with relation value (0.6800); patient P₄ suffered from malaria fever with relation value (0.6856).

Table 25. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: I—OWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problem	Chest Problem
P1	0.3676	0.6856	0.5260	0.0400	0.0656
P2	0.2000	0.0800	0.3760	0.6220	0.1696
P3	0.3500	0.6800	0.5700	0.0400	0.0500
P4	0.3676	0.6856	0.4400	0.2360	0.1240

Patient P₁ suffered from malaria fever with relation value (0.6856); patient P₂ suffered from stomach problems with relation value (0.6220); patient P₃ suffered from malaria fever with relation value (0.6800); patient P₄ suffered from malaria fever with relation value (0.6856).

Table 26. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: I—OWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3366	0.6396	0.4586	−0.2019	−0.3607
P2	−0.2005	−0.4005	0.0397	0.5789	−0.5600
P3	0.2971	0.5995	0.4989	−0.2019	−0.3011
P4	0.3366	0.6393	0.1995	−0.0609	−0.1414

Patient P₁ suffered from malaria fever with relation value (0.6396); patient P₂ suffered from stomach problems with relation value (0.5789); patient P₃ suffered from malaria fever with relation value (0.5995); patient P₄ suffered from malaria fever with relation value (0.6393).

Table 26. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: I—OWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3366	0.6396	0.4586	−0.2019	−0.3607
P2	−0.2005	−0.4005	0.0397	0.5789	−0.5600
P3	0.2971	0.5995	0.4989	−0.2019	−0.3011
P4	0.3366	0.6393	0.1995	−0.0609	−0.1414

Patient P₁ suffered from malaria fever with relation value (0.6396); patient P₂ suffered from stomach problems with relation value (0.5789); patient P₃ suffered from malaria fever with relation value (0.5995); patient P₄ suffered from malaria fever with relation value (0.6393).

Table 27. Score and Accuracy (Aggregation: I—OWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.34, 0.46〉	〈0.64, 0.76〉	〈0.46, 0.66〉	〈−0.2, 0.6〉	〈−0.36, 0.76〉
P2	〈−0.2, 0.8〉	〈−0.4, 0.8〉	〈0.04, 0.84〉	〈0.58, 0.7〉	〈−0.56, 0.96〉
P3	〈0.3, 0.5〉	〈0.6, 0.8〉	〈0.5, 0.7〉	〈−0.2, 0.6〉	〈−0.3, 0.7〉
P4	〈0.34, 0.46〉	〈0.64, 0.76〉	〈0.2, 0.8〉	〈−0.6, 0.74〉	〈−0.14, 0.66〉

Patient P₁ suffered from malaria fever with score (0.64); patient P₂ suffered from stomach problems with score (0.58); patient P₃ suffered from malaria fever with score (0.6); patient P₄ suffered from malaria fever with score (0.64).

Table 27. Score and Accuracy (Aggregation: I—OWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.34, 0.46〉	〈0.64, 0.76〉	〈0.46, 0.66〉	〈−0.2, 0.6〉	〈−0.36, 0.76〉
P2	〈−0.2, 0.8〉	〈−0.4, 0.8〉	〈0.04, 0.84〉	〈0.58, 0.7〉	〈−0.56, 0.96〉
P3	〈0.3, 0.5〉	〈0.6, 0.8〉	〈0.5, 0.7〉	〈−0.2, 0.6〉	〈−0.3, 0.7〉
P4	〈0.34, 0.46〉	〈0.64, 0.76〉	〈0.2, 0.8〉	〈−0.6, 0.74〉	〈−0.14, 0.66〉

Patient P₁ suffered from malaria fever with score (0.64); patient P₂ suffered from stomach problems with score (0.58); patient P₃ suffered from malaria fever with score (0.6); patient P₄ suffered from malaria fever with score (0.64).

Table 28. Membership and Non-membership degrees (Aggregation: q-ROFWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.56, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.56〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.44, 0.4〉	〈0.64, 0.0〉	〈0.2, 0.76〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.5, 0.3〉	〈0.34, 0.4〉	〈0.26, 0.4〉

Table 28. Membership and Non-membership degrees (Aggregation: q-ROFWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.56, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.56〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.44, 0.4〉	〈0.64, 0.0〉	〈0.2, 0.76〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.5, 0.3〉	〈0.34, 0.4〉	〈0.26, 0.4〉

Table 29. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: q-ROFWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.4000	0.7000	0.5289	0.0400	0.0649
P2	0.2000	0.0800	0.3791	0.6435	0.1684
P3	0.3501	0.6800	0.5700	0.0400	0.0500
P4	0.4000	0.7000	0.4400	0.2386	0.1262

Patient P₁ suffered from malaria fever with relation value (0.7000); patient P₂ suffered from stomach problems with relation value (0.6435); patient P₃ suffered from malaria fever with relation value (0.6800); patient P₄ suffered from malaria fever with relation value (0.7000).

Table 29. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: q-ROFWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.4000	0.7000	0.5289	0.0400	0.0649
P2	0.2000	0.0800	0.3791	0.6435	0.1684
P3	0.3501	0.6800	0.5700	0.0400	0.0500
P4	0.4000	0.7000	0.4400	0.2386	0.1262

Patient P₁ suffered from malaria fever with relation value (0.7000); patient P₂ suffered from stomach problems with relation value (0.6435); patient P₃ suffered from malaria fever with relation value (0.6800); patient P₄ suffered from malaria fever with relation value (0.7000).

Table 30. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: q-ROFWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3959	0.6989	0.4612	−0.2019	−0.3586
P2	−0.2005	−0.4005	0.0419	0.6419	−0.5584
P3	0.2971	0.5995	0.4989	−0.2019	−0.3011
P4	0.3959	0.6989	0.1995	−0.0590	−0.1398

Patient P₁ suffered from malaria fever with relation value (0.6989); patient P₂ suffered from stomach problems with relation value (0.6419); patient P₃ suffered from malaria fever with relation value (0.5995); patient P₄ suffered from malaria fever with relation value (0.6989).

Table 30. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: q-ROFWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3959	0.6989	0.4612	−0.2019	−0.3586
P2	−0.2005	−0.4005	0.0419	0.6419	−0.5584
P3	0.2971	0.5995	0.4989	−0.2019	−0.3011
P4	0.3959	0.6989	0.1995	−0.0590	−0.1398

Patient P₁ suffered from malaria fever with relation value (0.6989); patient P₂ suffered from stomach problems with relation value (0.6419); patient P₃ suffered from malaria fever with relation value (0.5995); patient P₄ suffered from malaria fever with relation value (0.6989).

Table 31. Score and Accuracy (Aggregation: q-ROFWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.4〉	〈0.7, 0.7〉	〈0.46, 0.66〉	〈−0.2, 0.6〉	〈−0.36, 0.76〉
P2	〈−0.2, 0.8〉	〈−0.4, 0.8〉	〈0.04, 0.84〉	〈0.64, 0.64〉	〈−0.56, 0.96〉
P3	〈0.3 0.5〉	〈0.6, 0.8〉	〈0.5, 0.7〉	〈−0.2, 0.6〉	〈−0.3, 0.7〉
P4	〈0.4, 0.4〉	〈0.7, 0.7〉	〈0.2, 0.8〉	〈−0.06, 0.74〉	〈−0.14, 0.66〉

Patient P₁ suffered from malaria fever with score (0.7); patient P₂ suffered from stomach problems with score (0.64); patient P₃ suffered from malaria fever with score (0.6); patient P₄ suffered from malaria fever with score (0.7).

Table 31. Score and Accuracy (Aggregation: q-ROFWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.4〉	〈0.7, 0.7〉	〈0.46, 0.66〉	〈−0.2, 0.6〉	〈−0.36, 0.76〉
P2	〈−0.2, 0.8〉	〈−0.4, 0.8〉	〈0.04, 0.84〉	〈0.64, 0.64〉	〈−0.56, 0.96〉
P3	〈0.3 0.5〉	〈0.6, 0.8〉	〈0.5, 0.7〉	〈−0.2, 0.6〉	〈−0.3, 0.7〉
P4	〈0.4, 0.4〉	〈0.7, 0.7〉	〈0.2, 0.8〉	〈−0.06, 0.74〉	〈−0.14, 0.66〉

Patient P₁ suffered from malaria fever with score (0.7); patient P₂ suffered from stomach problems with score (0.64); patient P₃ suffered from malaria fever with score (0.6); patient P₄ suffered from malaria fever with score (0.7).

Pythagorean Fuzzy Sets (q = 2)

Table 32. Membership and Non-membership degrees (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.05〉	〈0.7, 0.05〉	〈0.55, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.55〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.45, 0.4〉	〈0.65, 0.05〉	〈0.2, 0.75〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.05〉	〈0.7, 0.05〉	〈0.5, 0.3〉	〈0.35, 0.4〉	〈0.25, 0.4〉

Table 32. Membership and Non-membership degrees (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.05〉	〈0.7, 0.05〉	〈0.55, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.55〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.45, 0.4〉	〈0.65, 0.05〉	〈0.2, 0.75〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.05〉	〈0.7, 0.05〉	〈0.5, 0.3〉	〈0.35, 0.4〉	〈0.25, 0.4〉

Table 33. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3542	0.6644	0.4671	−0.1578	−0.2460
P2	−0.1062	−0.2648	0.1306	0.6121	−0.2729
P3	0.3089	0.6293	0.5206	−0.1578	−0.2213
P4	0.3542	0.6644	0.2563	0.0112	−0.1027

Patient P₁ suffered from malaria fever with relation value (06644); patient P₂ suffered from stomach problems with relation value (0.6121); patient P₃ suffered from malaria fever with relation value (0.6293); patient P₄ suffered from malaria fever with relation value (0.6644).

Table 33. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3542	0.6644	0.4671	−0.1578	−0.2460
P2	−0.1062	−0.2648	0.1306	0.6121	−0.2729
P3	0.3089	0.6293	0.5206	−0.1578	−0.2213
P4	0.3542	0.6644	0.2563	0.0112	−0.1027

Patient P₁ suffered from malaria fever with relation value (06644); patient P₂ suffered from stomach problems with relation value (0.6121); patient P₃ suffered from malaria fever with relation value (0.6293); patient P₄ suffered from malaria fever with relation value (0.6644).

Table 34. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3414	0.6445	0.4428	−0.2082	−0.3569
P2	−0.2070	−0.4064	0.0432	0.5938	−0.5544
P3	0.2915	0.5945	0.4933	−0.2082	−0.3074
P4	0.3414	0.6445	0.1930	−0.0575	−0.1580

Patient P₁ suffered from malaria fever with relation value (0.6445); patient P₂ suffered from stomach problems with relation value (0.5938); patient P₃ suffered from malaria fever with relation value (0.5945); patient P₄ suffered from malaria fever with relation value (0.6445).

Table 34. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3414	0.6445	0.4428	−0.2082	−0.3569
P2	−0.2070	−0.4064	0.0432	0.5938	−0.5544
P3	0.2915	0.5945	0.4933	−0.2082	−0.3074
P4	0.3414	0.6445	0.1930	−0.0575	−0.1580

Patient P₁ suffered from malaria fever with relation value (0.6445); patient P₂ suffered from stomach problems with relation value (0.5938); patient P₃ suffered from malaria fever with relation value (0.5945); patient P₄ suffered from malaria fever with relation value (0.6445).

Table 35. Score and Accuracy (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.157, 0.162〉	〈0.487, 0.492〉	〈0.29, 0.31〉	〈−0.12, 0.2〉	〈−0.26, 0.34〉
P2	〈−0.16, 0.34〉	〈−0.32, 0.4〉	〈0.04, 0.36〉	〈0.42, 0.425〉	〈−0.52, 0.6〉
P3	〈0.15, 0.17〉	〈0.48, 0.5〉	〈0.35, 0.37〉	〈−0.12, 0.2〉	〈−0.21, 0.29〉
P4	〈0.157, 0.162〉	〈0.487, 0.492〉	〈0.16, 0.34〉	〈−0.037, 0.282〉	〈−0.097, 0.22〉

Patient P₁ suffered from malaria fever with score (0.487); patient P₂ suffered from stomach problems with score (0.42); patient P₃ suffered from malaria fever with score (0.48); patient P₄ suffered from malaria fever with score (0.487).

Table 35. Score and Accuracy (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.157, 0.162〉	〈0.487, 0.492〉	〈0.29, 0.31〉	〈−0.12, 0.2〉	〈−0.26, 0.34〉
P2	〈−0.16, 0.34〉	〈−0.32, 0.4〉	〈0.04, 0.36〉	〈0.42, 0.425〉	〈−0.52, 0.6〉
P3	〈0.15, 0.17〉	〈0.48, 0.5〉	〈0.35, 0.37〉	〈−0.12, 0.2〉	〈−0.21, 0.29〉
P4	〈0.157, 0.162〉	〈0.487, 0.492〉	〈0.16, 0.34〉	〈−0.037, 0.282〉	〈−0.097, 0.22〉

Patient P₁ suffered from malaria fever with score (0.487); patient P₂ suffered from stomach problems with score (0.42); patient P₃ suffered from malaria fever with score (0.48); patient P₄ suffered from malaria fever with score (0.487).

Table 36. Membership and Non-membership degrees (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.545, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.54〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.44, 0.4〉	〈0.646, 0.0〉	〈0.2, 0.75〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.5, 0.3〉	〈0.34, 0.4〉	〈0.24, 0.4〉

Table 36. Membership and Non-membership degrees (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.545, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.54〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.44, 0.4〉	〈0.646, 0.0〉	〈0.2, 0.75〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.5, 0.3〉	〈0.34, 0.4〉	〈0.24, 0.4〉

Table 37. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.4000	0.7000	0.4622	−0.1578	−0.2440
P2	−0.1062	−0.2648	0.1238	0.6462	−0.2737
P3	0.3089	0.6293	0.5206	−0.1578	−0.2213
P4	0.4000	0.7000	0.2563	0.0029	−0.1138

Patient P₁ suffered from malaria fever with relation value (0.7000); patient P₂ suffered from stomach problems with relation value (0.6462); patient P₃ suffered from malaria fever with relation value (0.6293); patient P₄ suffered from malaria fever with relation value (0.7000).

Table 37. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.4000	0.7000	0.4622	−0.1578	−0.2440
P2	−0.1062	−0.2648	0.1238	0.6462	−0.2737
P3	0.3089	0.6293	0.5206	−0.1578	−0.2213
P4	0.4000	0.7000	0.2563	0.0029	−0.1138

Patient P₁ suffered from malaria fever with relation value (0.7000); patient P₂ suffered from stomach problems with relation value (0.6462); patient P₃ suffered from malaria fever with relation value (0.6293); patient P₄ suffered from malaria fever with relation value (0.7000).

Table 38. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3914	0.6944	0.4382	−0.2082	−0.3524
P2	−0.2070	−0.4064	0.0376	0.6399	−0.5512
P3	0.2915	0.5945	0.4933	−0.2082	−0.3074
P4	0.3914	0.6944	0.1930	−0.0647	−0.1681

Patient P₁ suffered from malaria fever with relation value (0.6944); patient P₂ suffered from stomach problems with relation value (0.6399); patient P₃ suffered from malaria fever with relation value (0.5945); patient P₄ suffered from malaria fever with relation value (0.6944).

Table 38. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3914	0.6944	0.4382	−0.2082	−0.3524
P2	−0.2070	−0.4064	0.0376	0.6399	−0.5512
P3	0.2915	0.5945	0.4933	−0.2082	−0.3074
P4	0.3914	0.6944	0.1930	−0.0647	−0.1681

Patient P₁ suffered from malaria fever with relation value (0.6944); patient P₂ suffered from stomach problems with relation value (0.6399); patient P₃ suffered from malaria fever with relation value (0.5945); patient P₄ suffered from malaria fever with relation value (0.6944).

Table 39. Score and Accuracy (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.16, 0.16〉	〈0.49, 0.49〉	〈0.287, 0.31〉	〈−0.12, 0.2〉	〈−0.257, 0.337〉
P2	〈−0.16, 0.34〉	〈−0.32, 0.4〉	〈0.037, 0.357〉	〈0.417, 0.417〉	〈−0.517, 0.597〉
P3	〈0.15, 0.17〉	〈0.48, 0.5〉	〈0.35, 0.37〉	〈−0.12, 0.2〉	〈−0.21, 0.29〉
P4	〈0.16, 0.16〉	〈0.49, 0.49〉	〈0.16, 0.34〉	〈−0.04, 0.277〉	〈−0.1, 0.217〉

Patient P₁ suffered from malaria fever with score (0.49); patient P₂ suffered from stomach problems with score (0.417); patient P₃ suffered from malaria fever with score (0.48); patient P₄ suffered from malaria fever with score (0.49).

Table 39. Score and Accuracy (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.16, 0.16〉	〈0.49, 0.49〉	〈0.287, 0.31〉	〈−0.12, 0.2〉	〈−0.257, 0.337〉
P2	〈−0.16, 0.34〉	〈−0.32, 0.4〉	〈0.037, 0.357〉	〈0.417, 0.417〉	〈−0.517, 0.597〉
P3	〈0.15, 0.17〉	〈0.48, 0.5〉	〈0.35, 0.37〉	〈−0.12, 0.2〉	〈−0.21, 0.29〉
P4	〈0.16, 0.16〉	〈0.49, 0.49〉	〈0.16, 0.34〉	〈−0.04, 0.277〉	〈−0.1, 0.217〉

Patient P₁ suffered from malaria fever with score (0.49); patient P₂ suffered from stomach problems with score (0.417); patient P₃ suffered from malaria fever with score (0.48); patient P₄ suffered from malaria fever with score (0.49).

Table 40. Membership and Non-membership degrees (Aggregation: Bellaman/Zadeh).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.5, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.4, 0.4〉	〈0.6, 0.0〉	〈0.2, 0.7〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.5, 0.3〉	〈0.3, 0.4〉	〈0.2, 0.4〉

Table 40. Membership and Non-membership degrees (Aggregation: Bellaman/Zadeh).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.5, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.4, 0.4〉	〈0.6, 0.0〉	〈0.2, 0.7〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.5, 0.3〉	〈0.3, 0.4〉	〈0.2, 0.4〉

Table 41. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: Bellaman/Zadeh).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.4000	0.7000	0.4140	−0.1578	−0.2213
P2	−0.1062	−0.2648	0.0702	0.6000	−0.2799
P3	0.3089	0.6293	0.5206	−0.5178	−0.2213
P4	0.4000	0.7000	0.2563	−0.0464	−0.1578

Patient P₁ suffered from malaria fever with relation value (0.7000); patient P₂ suffered from stomach problems with relation value (0.6000); patient P₃ suffered from malaria fever with relation value (0.6293); patient P₄ suffered from malaria fever with relation value (0.7000).

Table 41. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: Bellaman/Zadeh).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.4000	0.7000	0.4140	−0.1578	−0.2213
P2	−0.1062	−0.2648	0.0702	0.6000	−0.2799
P3	0.3089	0.6293	0.5206	−0.5178	−0.2213
P4	0.4000	0.7000	0.2563	−0.0464	−0.1578

Patient P₁ suffered from malaria fever with relation value (0.7000); patient P₂ suffered from stomach problems with relation value (0.6000); patient P₃ suffered from malaria fever with relation value (0.6293); patient P₄ suffered from malaria fever with relation value (0.7000).

Table 42. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: Bellaman/Zadeh).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3914	0.6944	0.3923	−0.2082	−0.3074
P2	−0.2070	−0.4064	−0.0072	0.5932	−0.5052
P3	0.2915	0.5945	0.4933	−0.2082	−0.3074
P4	0.3914	0.6944	0.1930	−0.1078	−0.2082

Patient P₁ suffered from malaria fever with relation value (0.6944); patient P₂ suffered from stomach problems with relation value (0.5932); patient P₃ suffered from malaria fever with relation value (0.5945); patient P₄ suffered from malaria fever with relation value (0.6944).

Table 42. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: Bellaman/Zadeh).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3914	0.6944	0.3923	−0.2082	−0.3074
P2	−0.2070	−0.4064	−0.0072	0.5932	−0.5052
P3	0.2915	0.5945	0.4933	−0.2082	−0.3074
P4	0.3914	0.6944	0.1930	−0.1078	−0.2082

Patient P₁ suffered from malaria fever with relation value (0.6944); patient P₂ suffered from stomach problems with relation value (0.5932); patient P₃ suffered from malaria fever with relation value (0.5945); patient P₄ suffered from malaria fever with relation value (0.6944).

Table 43. Score and Accuracy (Aggregation: Bellaman/Zadeh).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.16, 0.16〉	〈0.49, 0.49〉	〈0.24, 0.26〉	〈−0.12, 0.2〉	〈−0.21, 0.29〉
P2	〈−0.16, 0.34〉	〈−0.32, 0.4〉	〈0.0, 0.32〉	〈0.36, 0.36〉	〈−0.45, 0.53〉
P3	〈0.15, 0.17〉	〈0.48, 0.5〉	〈0.35, 0.37〉	〈−0.12, 0.2〉	〈−0.21, 0.29〉
P4	〈0.16, 0.16〉	〈0.49, 0.49〉	〈0.16, 0.34〉	〈−0.07, 0.25〉	〈−0.12, 0.2〉

Patient P₁ suffered from malaria fever with score (0.49); patient P₂ suffered from stomach problems with score (0.36); patient P₃ suffered from malaria fever with score (0.48); patient P₄ suffered from malaria fever with score (0.49).

Table 43. Score and Accuracy (Aggregation: Bellaman/Zadeh).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.16, 0.16〉	〈0.49, 0.49〉	〈0.24, 0.26〉	〈−0.12, 0.2〉	〈−0.21, 0.29〉
P2	〈−0.16, 0.34〉	〈−0.32, 0.4〉	〈0.0, 0.32〉	〈0.36, 0.36〉	〈−0.45, 0.53〉
P3	〈0.15, 0.17〉	〈0.48, 0.5〉	〈0.35, 0.37〉	〈−0.12, 0.2〉	〈−0.21, 0.29〉
P4	〈0.16, 0.16〉	〈0.49, 0.49〉	〈0.16, 0.34〉	〈−0.07, 0.25〉	〈−0.12, 0.2〉

Patient P₁ suffered from malaria fever with score (0.49); patient P₂ suffered from stomach problems with score (0.36); patient P₃ suffered from malaria fever with score (0.48); patient P₄ suffered from malaria fever with score (0.49).

Table 44. Membership and Non-membership degrees (Aggregation: I—OWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.06〉	〈0.7, 0.06〉	〈0.56, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.56〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.44, 0.4〉	〈0.64, 0.06〉	〈0.2, 0.76〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.06〉	〈0.7, 0.06〉	〈0.5, 0.3〉	〈0.34, 0.4〉	〈0.26, 0.4〉

Table 44. Membership and Non-membership degrees (Aggregation: I—OWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.06〉	〈0.7, 0.06〉	〈0.56, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.56〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.44, 0.4〉	〈0.64, 0.06〉	〈0.2, 0.76〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.06〉	〈0.7, 0.06〉	〈0.5, 0.3〉	〈0.34, 0.4〉	〈0.26, 0.4〉

Table 45. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: I—OWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3451	0.6573	0.4778	−0.1578	−0.2502
P2	−0.1062	−0.2648	0.1184	0.5940	−0.2700
P3	0.3089	0.6293	0.5206	−0.1578	−0.2213
P4	0.3451	0.6573	0.2563	−0.0004	−0.0915

Patient P₁ suffered from malaria fever with relation value (0.6573); patient P₂ suffered from stomach problems with relation value (0.5940); patient P₃ suffered from malaria fever with relation value (0.6293); patient P₄ suffered from malaria fever with relation value (0.6573).

Table 45. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: I—OWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3451	0.6573	0.4778	−0.1578	−0.2502
P2	−0.1062	−0.2648	0.1184	0.5940	−0.2700
P3	0.3089	0.6293	0.5206	−0.1578	−0.2213
P4	0.3451	0.6573	0.2563	−0.0004	−0.0915

Patient P₁ suffered from malaria fever with relation value (0.6573); patient P₂ suffered from stomach problems with relation value (0.5940); patient P₃ suffered from malaria fever with relation value (0.6293); patient P₄ suffered from malaria fever with relation value (0.6573).

Table 46. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: I—OWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3314	0.6345	0.4529	−0.2082	−0.3668
P2	−0.2070	−0.4064	0.0332	0.5737	−0.5643
P3	0.2915	0.5945	0.4933	−0.2082	−0.3074
P4	0.3314	0.6345	0.1930	−0.0676	−0.1480

Patient P₁ suffered from malaria fever with relation value (0.6345); patient P₂ suffered from stomach problems with relation value (0.5737); patient P₃ suffered from malaria fever with relation value (0.5945); patient P₄ suffered from malaria fever with relation value (0.6345).

Table 46. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: I—OWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3314	0.6345	0.4529	−0.2082	−0.3668
P2	−0.2070	−0.4064	0.0332	0.5737	−0.5643
P3	0.2915	0.5945	0.4933	−0.2082	−0.3074
P4	0.3314	0.6345	0.1930	−0.0676	−0.1480

Patient P₁ suffered from malaria fever with relation value (0.6345); patient P₂ suffered from stomach problems with relation value (0.5737); patient P₃ suffered from malaria fever with relation value (0.5945); patient P₄ suffered from malaria fever with relation value (0.6345).

Table 47. Score and Accuracy (Aggregation: I—OWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.156, 0.163〉	〈0.486, 0.493〉	〈0.3, 0.32〉	〈−0.12, 0.2〉	〈−0.273, 0.353〉
P2	〈−0.16, 0.34〉	〈−0.32, 0.4〉	〈0.03, 0.35〉	〈0.4, 0.41〉	〈−0.547, 0.617〉
P3	〈0.15, 0.16〉	〈0.48, 0.5〉	〈0.35, 0.37〉	〈−0.12, 0.2〉	〈−0.21, 0.29〉
P4	〈0.156, 0.163〉	〈0.486, 0.493〉	〈0.16, 0.34〉	〈−0.04, 0.27〉	〈−0.09, 0.227〉

Patient P₁ suffered from malaria fever with score (0.486); patient P₂ suffered from stomach problems with score (0.4); patient P₃ suffered from malaria fever with score (0.48); patient P₄ suffered from malaria fever with score (0.486).

Table 47. Score and Accuracy (Aggregation: I—OWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.156, 0.163〉	〈0.486, 0.493〉	〈0.3, 0.32〉	〈−0.12, 0.2〉	〈−0.273, 0.353〉
P2	〈−0.16, 0.34〉	〈−0.32, 0.4〉	〈0.03, 0.35〉	〈0.4, 0.41〉	〈−0.547, 0.617〉
P3	〈0.15, 0.16〉	〈0.48, 0.5〉	〈0.35, 0.37〉	〈−0.12, 0.2〉	〈−0.21, 0.29〉
P4	〈0.156, 0.163〉	〈0.486, 0.493〉	〈0.16, 0.34〉	〈−0.04, 0.27〉	〈−0.09, 0.227〉

Patient P₁ suffered from malaria fever with score (0.486); patient P₂ suffered from stomach problems with score (0.4); patient P₃ suffered from malaria fever with score (0.48); patient P₄ suffered from malaria fever with score (0.486).

Table 48. Membership and Non-membership degrees (Aggregation: q-ROFWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.36, 0.0〉	〈0.36, 0.0〉	〈0.3, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.557〉
P2	〈0.1, 0.5〉	〈0.1, 0.6〉	〈0.2, 0.4〉	〈0.21, 0.0〉	〈0.2, 0.758〉
P3	〈0.3, 0.1〉	〈0.293, 0.1〉	〈0.32, 0.1〉	〈0.2, 0.4〉	〈0.1, 0.5〉
P4	〈0.245, 0.0〉	〈0.245, 0.0〉	〈0.21, 0.3〉	〈0.2, 0.4〉	〈0.2, 0.4〉

Table 48. Membership and Non-membership degrees (Aggregation: q-ROFWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.36, 0.0〉	〈0.36, 0.0〉	〈0.3, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.557〉
P2	〈0.1, 0.5〉	〈0.1, 0.6〉	〈0.2, 0.4〉	〈0.21, 0.0〉	〈0.2, 0.758〉
P3	〈0.3, 0.1〉	〈0.293, 0.1〉	〈0.32, 0.1〉	〈0.2, 0.4〉	〈0.1, 0.5〉
P4	〈0.245, 0.0〉	〈0.245, 0.0〉	〈0.21, 0.3〉	〈0.2, 0.4〉	〈0.2, 0.4〉

Table 49. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: q-ROFWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3606	0.3606	0.2051	−0.1578	−0.2493
P2	−0.3301	−0.3777	−0.1578	0.2078	−0.2705
P3	0.2051	0.1980	0.2258	−0.1578	−0.3301
P4	0.2450	0.2450	−0.0715	−0.1578	−0.1578

In patient P₁, the diseases viral fever and malaria fever showed the same relation value (0.3606), so, it was not obvious which disease P₁ was suffering from. Patient P₂ suffered from stomach problems with relation value (0.2078); patient P₃ suffered from typhoid fever with relation value (0.2258). In patient P₄, the diseases viral fever and malaria fever showed the same relation value (0.2450), so, it was not obvious which disease P₄ was suffering from.

Table 49. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: q-ROFWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3606	0.3606	0.2051	−0.1578	−0.2493
P2	−0.3301	−0.3777	−0.1578	0.2078	−0.2705
P3	0.2051	0.1980	0.2258	−0.1578	−0.3301
P4	0.2450	0.2450	−0.0715	−0.1578	−0.1578

In patient P₁, the diseases viral fever and malaria fever showed the same relation value (0.3606), so, it was not obvious which disease P₁ was suffering from. Patient P₂ suffered from stomach problems with relation value (0.2078); patient P₃ suffered from typhoid fever with relation value (0.2258). In patient P₄, the diseases viral fever and malaria fever showed the same relation value (0.2450), so, it was not obvious which disease P₄ was suffering from.

Table 50. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: q-ROFWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3517	0.3517	0.1909	−0.2082	−0.3647
P2	−0.4077	−0.5081	−0.2082	0.1982	−0.5627
P3	0.1909	0.1839	0.2110	−0.2082	−0.4077
P4	0.2355	0.2355	−0.1011	−0.2082	−0.2082

In patient P₁, the diseases viral fever and malaria fever showed the same relation value (0.3517), so, it was not obvious which disease P₁ was suffering from. Patient P₂ suffered from stomach problems with relation value (0.1982); patient P₃ suffered from typhoid fever with relation value (0.2110). In patient P₄, the diseases viral fever and malaria fever showed the same relation value (0.2355), so, it was not obvious which disease P₄ was suffering from.

Table 50. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: q-ROFWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3517	0.3517	0.1909	−0.2082	−0.3647
P2	−0.4077	−0.5081	−0.2082	0.1982	−0.5627
P3	0.1909	0.1839	0.2110	−0.2082	−0.4077
P4	0.2355	0.2355	−0.1011	−0.2082	−0.2082

In patient P₁, the diseases viral fever and malaria fever showed the same relation value (0.3517), so, it was not obvious which disease P₁ was suffering from. Patient P₂ suffered from stomach problems with relation value (0.1982); patient P₃ suffered from typhoid fever with relation value (0.2110). In patient P₄, the diseases viral fever and malaria fever showed the same relation value (0.2355), so, it was not obvious which disease P₄ was suffering from.

Table 51. Score and Accuracy (Aggregation: q-ROFWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.13, 0.13〉	〈0.13, 0.13〉	〈0.08, 0.1〉	〈−0.12, 0.2〉	〈−0.271, 0.351〉
P2	〈−0.24, 0.26〉	〈−0.35, 0.37〉	〈−0.12, 0.2〉	〈0.043, 0.043〉	〈−0.535, 0.615〉
P3	〈0.08, 0.1〉	〈0.075, 0.095〉	〈0.092, 0.112〉	〈−0.12, 0.2〉	〈−0.24, 0.26〉
P4	〈0.06, 0.06〉	〈0.06, 0.06〉	〈−0.046, 0.133〉	〈−0.12, 0.2〉	〈−0.12, 0.2〉

In patient P₁, the diseases viral fever and malaria fever showed the same score and same accuracy (0.13, 0.13), so, it was not obvious which disease P₁ was suffering from. Patient P₂ suffered from stomach problems with score (0.043); patient P₃ suffered from typhoid fever with score (0.092). In patient P₄, the diseases viral fever and malaria fever showed the same score and accuracy (0.06, 0.6); so, it was not obvious which disease P₄ was suffering from.

Table 51. Score and Accuracy (Aggregation: q-ROFWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.13, 0.13〉	〈0.13, 0.13〉	〈0.08, 0.1〉	〈−0.12, 0.2〉	〈−0.271, 0.351〉
P2	〈−0.24, 0.26〉	〈−0.35, 0.37〉	〈−0.12, 0.2〉	〈0.043, 0.043〉	〈−0.535, 0.615〉
P3	〈0.08, 0.1〉	〈0.075, 0.095〉	〈0.092, 0.112〉	〈−0.12, 0.2〉	〈−0.24, 0.26〉
P4	〈0.06, 0.06〉	〈0.06, 0.06〉	〈−0.046, 0.133〉	〈−0.12, 0.2〉	〈−0.12, 0.2〉

In patient P₁, the diseases viral fever and malaria fever showed the same score and same accuracy (0.13, 0.13), so, it was not obvious which disease P₁ was suffering from. Patient P₂ suffered from stomach problems with score (0.043); patient P₃ suffered from typhoid fever with score (0.092). In patient P₄, the diseases viral fever and malaria fever showed the same score and accuracy (0.06, 0.6); so, it was not obvious which disease P₄ was suffering from.

Fermatean Fuzzy Sets (q = 3)

Table 52. Membership and Non-membership degrees (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.05〉	〈0.7, 0.05〉	〈0.55, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.55〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.45, 0.4〉	〈0.65, 0.05〉	〈0.2, 0.75〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.05〉	〈0.7, 0.05〉	〈0.5, 0.3〉	〈0.35, 0.4〉	〈0.25, 0.4〉

Table 52. Membership and Non-membership degrees (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.05〉	〈0.7, 0.05〉	〈0.55, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.55〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.45, 0.4〉	〈0.65, 0.05〉	〈0.2, 0.75〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.05〉	〈0.7, 0.05〉	〈0.5, 0.3〉	〈0.35, 0.4〉	〈0.25, 0.4〉

Table 53. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3511	0.6565	0.4559	−0.1902	−0.3160
P2	−0.1733	−0.3514	0.0719	0.6051	−0.4219
P3	0.3022	0.6131	0.5078	−0.1902	−0.2768
P4	0.3511	0.6565	0.2160	−0.0352	−0.1391

Patient P₁ suffered from malaria fever with relation value (0.6565); patient P₂ suffered from stomach problems with relation value (0.6051); patient P₃ suffered from malaria fever with relation value (0.6131); patient P₄ suffered from malaria fever with relation value (0.6565).

Table 53. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3511	0.6565	0.4559	−0.1902	−0.3160
P2	−0.1733	−0.3514	0.0719	0.6051	−0.4219
P3	0.3022	0.6131	0.5078	−0.1902	−0.2768
P4	0.3511	0.6565	0.2160	−0.0352	−0.1391

Patient P₁ suffered from malaria fever with relation value (0.6565); patient P₂ suffered from stomach problems with relation value (0.6051); patient P₃ suffered from malaria fever with relation value (0.6131); patient P₄ suffered from malaria fever with relation value (0.6565).

Table 54. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3404	0.6422	0.4410	−0.2096	−0.3590
P2	−0.2091	−0.4086	0.0409	0.5917	−0.5572
P3	0.2904	0.5922	0.4913	−0.2096	−0.3092
P4	0.3404	0.6422	0.1909	−0.0594	−0.1595

Patient P₁ suffered from malaria fever with relation value (0.6422); patient P₂ suffered from stomach problems with relation value (0.5917); patient P₃ suffered from malaria fever with relation value (0.5922); patient P₄ suffered from malaria fever with relation value (0.6422).

Table 54. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3404	0.6422	0.4410	−0.2096	−0.3590
P2	−0.2091	−0.4086	0.0409	0.5917	−0.5572
P3	0.2904	0.5922	0.4913	−0.2096	−0.3092
P4	0.3404	0.6422	0.1909	−0.0594	−0.1595

Patient P₁ suffered from malaria fever with relation value (0.6422); patient P₂ suffered from stomach problems with relation value (0.5917); patient P₃ suffered from malaria fever with relation value (0.5922); patient P₄ suffered from malaria fever with relation value (0.6422).

Table 55. Score and Accuracy (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.063, 0.064〉	〈0.342, 0.343〉	〈0.165, 0.167〉	〈−0.056, 0.072〉	〈−0.158, 0.174〉
P2	〈−0.098, 0.152〉	〈−0.2, 0.224〉	〈0.027, 0.155〉	〈0.2745, 0.2747〉	〈−0.413, 0.429〉
P3	〈0.063, 0.065〉	〈0.342, 0.344〉	〈0.215, 0.217〉	〈−0.05, 0.072〉	〈−0.117, 0.133〉
P4	〈0.063, 0.064〉	〈0.342, 0.343〉	〈0.098, 0.152〉	〈−0.02, 0.1〉	〈−0.048, 0.079〉

Patient P₁ suffered from malaria fever with score (0.342); patient P₂ suffered from stomach problems with score (0.2745); patient P₃ suffered from malaria fever with score (0.342); patient P₄ suffered from malaria fever with score (0.3426).

Table 55. Score and Accuracy (Aggregation: Arithmetic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.063, 0.064〉	〈0.342, 0.343〉	〈0.165, 0.167〉	〈−0.056, 0.072〉	〈−0.158, 0.174〉
P2	〈−0.098, 0.152〉	〈−0.2, 0.224〉	〈0.027, 0.155〉	〈0.2745, 0.2747〉	〈−0.413, 0.429〉
P3	〈0.063, 0.065〉	〈0.342, 0.344〉	〈0.215, 0.217〉	〈−0.05, 0.072〉	〈−0.117, 0.133〉
P4	〈0.063, 0.064〉	〈0.342, 0.343〉	〈0.098, 0.152〉	〈−0.02, 0.1〉	〈−0.048, 0.079〉

Patient P₁ suffered from malaria fever with score (0.342); patient P₂ suffered from stomach problems with score (0.2745); patient P₃ suffered from malaria fever with score (0.342); patient P₄ suffered from malaria fever with score (0.3426).

Table 56. Membership and Non-membership degrees (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.54, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.545〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.44, 0.4〉	〈0.646, 0.0〉	〈0.2, 0.746〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.5, 0.3〉	〈0.342, 0.4〉	〈0.24, 0.4〉

Table 56. Membership and Non-membership degrees (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.54, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.545〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.44, 0.4〉	〈0.646, 0.0〉	〈0.2, 0.746〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.5, 0.3〉	〈0.342, 0.4〉	〈0.24, 0.4〉

Table 57. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.4000	0.7000	0.4512	−0.1902	−0.3125
P2	−0.1733	−0.3514	0.0658	0.6462	−0.4212
P3	0.3022	0.6131	0.5078	−0.1902	−0.2768
P4	0.4000	0.7000	0.2160	−0.0427	−0.1493

Patient P₁ suffered from malaria fever with relation value (0.7000); patient P₂ suffered from stomach problems with relation value (0.6462); patient P₃ suffered from malaria fever with relation value (0.6131); patient P₄ suffered from malaria fever with relation value (0.7000).

Table 57. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.4000	0.7000	0.4512	−0.1902	−0.3125
P2	−0.1733	−0.3514	0.0658	0.6462	−0.4212
P3	0.3022	0.6131	0.5078	−0.1902	−0.2768
P4	0.4000	0.7000	0.2160	−0.0427	−0.1493

Patient P₁ suffered from malaria fever with relation value (0.7000); patient P₂ suffered from stomach problems with relation value (0.6462); patient P₃ suffered from malaria fever with relation value (0.6131); patient P₄ suffered from malaria fever with relation value (0.7000).

Table 58. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3904	0.6922	0.4364	−0.2096	−0.3544
P2	−0.2019	−0.4086	0.0353	0.6378	−0.5539
P3	0.2904	0.5922	0.4913	−0.2096	−0.3092
P4	0.3904	0.6922	0.1909	−0.0665	−0.1695

Patient P₁ suffered from malaria fever with relation value (0.6922); patient P₂ suffered from stomach problems with relation value (0.6378); patient P₃ suffered from malaria fever with relation value (0.5922); patient P₄ suffered from malaria fever with relation value (0.6922).

Table 58. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3904	0.6922	0.4364	−0.2096	−0.3544
P2	−0.2019	−0.4086	0.0353	0.6378	−0.5539
P3	0.2904	0.5922	0.4913	−0.2096	−0.3092
P4	0.3904	0.6922	0.1909	−0.0665	−0.1695

Patient P₁ suffered from malaria fever with relation value (0.6922); patient P₂ suffered from stomach problems with relation value (0.6378); patient P₃ suffered from malaria fever with relation value (0.5922); patient P₄ suffered from malaria fever with relation value (0.6922).

Table 59. Score and Accuracy (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.064, 0.064〉	〈0.343, 0.343〉	〈0.161, 0.163〉	〈−0.05, 0.07〉	〈−0.15, 0.17〉
P2	〈−0.1, 0.152〉	〈−0.2, 0.22〉	〈0.02, 0.15〉	〈0.27, 0.27〉	〈−0.4, 0.42〉
P3	〈0.063, 0.065〉	〈0.342, 0.344〉	〈0.215, 0.217〉	〈−0.05, 0.07〉	〈−0.12, 0.13〉
P4	〈0.064, 0.064〉	〈0.343, 0.343〉	〈0.098, 0.15〉	〈−0.02, 0.1〉	〈−0.05, 0.077〉

Patient P₁ suffered from malaria fever with score (0.343); patient P₂ suffered from stomach problems with score (0.27); patient P₃ suffered from malaria fever with score (0.342); patient P₄ suffered from malaria fever with score (0.343).

Table 59. Score and Accuracy (Aggregation: Harmonic Mean).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.064, 0.064〉	〈0.343, 0.343〉	〈0.161, 0.163〉	〈−0.05, 0.07〉	〈−0.15, 0.17〉
P2	〈−0.1, 0.152〉	〈−0.2, 0.22〉	〈0.02, 0.15〉	〈0.27, 0.27〉	〈−0.4, 0.42〉
P3	〈0.063, 0.065〉	〈0.342, 0.344〉	〈0.215, 0.217〉	〈−0.05, 0.07〉	〈−0.12, 0.13〉
P4	〈0.064, 0.064〉	〈0.343, 0.343〉	〈0.098, 0.15〉	〈−0.02, 0.1〉	〈−0.05, 0.077〉

Patient P₁ suffered from malaria fever with score (0.343); patient P₂ suffered from stomach problems with score (0.27); patient P₃ suffered from malaria fever with score (0.342); patient P₄ suffered from malaria fever with score (0.343).

Table 60. Membership and Non-membership degrees (Aggregation: Bellaman/Zadeh).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.5, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.4, 0.4〉	〈0.6, 0.0〉	〈0.2, 0.7〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.5, 0.3〉	〈0.3, 0.4〉	〈0.2, 0.4〉

Table 60. Membership and Non-membership degrees (Aggregation: Bellaman/Zadeh).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.5, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.4, 0.4〉	〈0.6, 0.0〉	〈0.2, 0.7〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.0〉	〈0.7, 0.0〉	〈0.5, 0.3〉	〈0.3, 0.4〉	〈0.2, 0.4〉

Table 61. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: Bellaman/Zadeh).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.4000	0.7000	0.4044	−0.1902	−0.2768
P2	−0.1733	−0.3514	0.0179	0.6000	−0.4061
P3	0.3022	0.6131	0.5078	−0.1902	−0.2786
P4	0.4000	0.7000	0.2160	−0.0875	−0.1902

Patient P₁ suffered from malaria fever with relation value (0.7000); patient P₂ suffered from stomach problems with relation value (0.6000); patient P₃ suffered from malaria fever with relation value (0.6131); patient P₄ suffered from malaria fever with relation value (0.7000).

Table 61. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: Bellaman/Zadeh).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.4000	0.7000	0.4044	−0.1902	−0.2768
P2	−0.1733	−0.3514	0.0179	0.6000	−0.4061
P3	0.3022	0.6131	0.5078	−0.1902	−0.2786
P4	0.4000	0.7000	0.2160	−0.0875	−0.1902

Patient P₁ suffered from malaria fever with relation value (0.7000); patient P₂ suffered from stomach problems with relation value (0.6000); patient P₃ suffered from malaria fever with relation value (0.6131); patient P₄ suffered from malaria fever with relation value (0.7000).

Table 62. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: Bellaman/Zadeh).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3904	0.6922	0.3907	−0.2096	−0.3092
P2	−0.2091	−0.4086	−0.0092	0.5913	−0.5078
P3	0.2904	0.5922	0.4913	−0.2096	−0.3092
P4	0.3904	0.6922	0.1909	−0.1095	−0.2096

Patient P₁ suffered from malaria fever with relation value (0.6922); patient P₂ suffered from stomach problems with relation value (0.5913); patient P₃ suffered from malaria fever with relation value (0.5922); patient P₄ suffered from malaria fever with relation value (0.6922).

Table 62. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: Bellaman/Zadeh).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3904	0.6922	0.3907	−0.2096	−0.3092
P2	−0.2091	−0.4086	−0.0092	0.5913	−0.5078
P3	0.2904	0.5922	0.4913	−0.2096	−0.3092
P4	0.3904	0.6922	0.1909	−0.1095	−0.2096

Patient P₁ suffered from malaria fever with relation value (0.6922); patient P₂ suffered from stomach problems with relation value (0.5913); patient P₃ suffered from malaria fever with relation value (0.5922); patient P₄ suffered from malaria fever with relation value (0.6922).

Table 63. Score and Accuracy (Aggregation: Bellaman/Zadeh).

Patient\ Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.064, 0.064〉	〈0.343, 0.343〉	〈0.124, 0.126〉	〈−0.056, 0.07〉	〈−0.117, 0.13〉
P2	〈−0.098, 0.152〉	〈−0.2, 0.22〉	〈0.0, 0.128〉	〈0.21, 0.21〉	〈−0.33, 0.35〉
P3	〈0.063, 0.065〉	〈0.342, 0.344〉	〈0.215, 0.217〉	〈−0.056, 0.07〉	〈−0.117, 0.13〉
P4	〈0.064, 0.064〉	〈0.343, 0.343〉	〈0.098, 0.15〉	〈−0.037, 0.1〉	〈−0.056, 0.072〉

Patient P₁ suffered from malaria fever with score (0.343); patient P₂ suffered from stomach problems with score (0.21); patient P₃ suffered from malaria fever with score (0.342); patient P₄ suffered from malaria fever with score (0.343).

Table 63. Score and Accuracy (Aggregation: Bellaman/Zadeh).

Patient\ Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.064, 0.064〉	〈0.343, 0.343〉	〈0.124, 0.126〉	〈−0.056, 0.07〉	〈−0.117, 0.13〉
P2	〈−0.098, 0.152〉	〈−0.2, 0.22〉	〈0.0, 0.128〉	〈0.21, 0.21〉	〈−0.33, 0.35〉
P3	〈0.063, 0.065〉	〈0.342, 0.344〉	〈0.215, 0.217〉	〈−0.056, 0.07〉	〈−0.117, 0.13〉
P4	〈0.064, 0.064〉	〈0.343, 0.343〉	〈0.098, 0.15〉	〈−0.037, 0.1〉	〈−0.056, 0.072〉

Patient P₁ suffered from malaria fever with score (0.343); patient P₂ suffered from stomach problems with score (0.21); patient P₃ suffered from malaria fever with score (0.342); patient P₄ suffered from malaria fever with score (0.343).

Table 64. Membership and Non-membership degrees (Aggregation: I—OWA).

Patient\ Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.06〉	〈0.7, 0.06〉	〈0.56, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.56〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.44, 0.4〉	〈0.64, 0.06〉	〈0.2, 0.76〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.06〉	〈0.7, 0.06〉	〈0.5, 0.3〉	〈0.34, 0.4〉	〈0.26, 0.4〉

Table 64. Membership and Non-membership degrees (Aggregation: I—OWA).

Patient\ Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.4, 0.06〉	〈0.7, 0.06〉	〈0.56, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.56〉
P2	〈0.3, 0.5〉	〈0.2, 0.6〉	〈0.44, 0.4〉	〈0.64, 0.06〉	〈0.2, 0.76〉
P3	〈0.4, 0.1〉	〈0.7, 0.1〉	〈0.6, 0.1〉	〈0.2, 0.4〉	〈0.2, 0.5〉
P4	〈0.4, 0.06〉	〈0.7, 0.06〉	〈0.5, 0.3〉	〈0.34, 0.4〉	〈0.26, 0.4〉

Table 65. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: I—OWA).

Patient\ Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3413	0.6478	0.4663	−0.1902	−0.3234
P2	−0.1733	−0.3514	0.0610	0.5858	−0.4238
P3	0.3022	0.6131	0.5078	−0.1902	−0.2768
P4	0.3413	0.6478	0.2160	−0.0457	−0.1288

Patient P₁ suffered from malaria fever with relation value (0.6478); patient P₂ suffered from stomach problems with relation value (0.5858); patient P₃ suffered from malaria fever with relation value (0.6131); patient P₄ suffered from malaria fever with relation value (0.6478).

Table 65. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: I—OWA).

Patient\ Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3413	0.6478	0.4663	−0.1902	−0.3234
P2	−0.1733	−0.3514	0.0610	0.5858	−0.4238
P3	0.3022	0.6131	0.5078	−0.1902	−0.2768
P4	0.3413	0.6478	0.2160	−0.0457	−0.1288

Patient P₁ suffered from malaria fever with relation value (0.6478); patient P₂ suffered from stomach problems with relation value (0.5858); patient P₃ suffered from malaria fever with relation value (0.6131); patient P₄ suffered from malaria fever with relation value (0.6478).

Table 66. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: I—OWA).

Patient\ Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3304	0.6322	0.4511	−0.2096	−0.3689
P2	−0.2091	−0.4086	0.0309	0.5716	−0.5671
P3	0.2904	0.5922	0.4913	−0.2096	−0.3092
P4	0.3304	0.6322	0.1909	−0.0694	−0.1495

Patient P₁ suffered from malaria fever with relation value (0.6322); patient P₂ suffered from stomach problems with relation value (0.5716); patient P₃ suffered from malaria fever with relation value (0.5922); patient P₄ suffered from malaria fever with relation value (0.6322).

Table 66. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: I—OWA).

Patient\ Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.3304	0.6322	0.4511	−0.2096	−0.3689
P2	−0.2091	−0.4086	0.0309	0.5716	−0.5671
P3	0.2904	0.5922	0.4913	−0.2096	−0.3092
P4	0.3304	0.6322	0.1909	−0.0694	−0.1495

Patient P₁ suffered from malaria fever with relation value (0.6322); patient P₂ suffered from stomach problems with relation value (0.5716); patient P₃ suffered from malaria fever with relation value (0.5922); patient P₄ suffered from malaria fever with relation value (0.6322).

Table 67. Score and Accuracy (Aggregation: I—OWA).

Patient\ Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.063, 0.064〉	〈0.342, 0.343〉	〈0.174. 0.176〉	〈−0.056, 0.072〉	〈−0.167, 0.18〉
P2	〈−0.098, 0.152〉	〈−0.2, 0.224〉	〈0.02, 0.149〉	〈0.261, 0.262〉	〈−0.43, 0.44〉
P3	〈0.063, 0.065〉	〈0.342, 0.344〉	〈0.215, 0.217〉	〈−0.05, 0.07〉	〈−0.11, 0.13〉
P4	〈0.063, 0.064〉	〈0.342, 0.343〉	〈0.098, 0.15〉	〈−0.024, 0.1〉	〈−0.046, 0.08〉

Patient P₁ suffered from malaria fever with score (0.342); patient P₂ suffered from stomach problems with score (0.261); patient P₃ suffered from malaria fever with score (0.342); patient P₄ suffered from malaria fever with score (0.342).

Table 67. Score and Accuracy (Aggregation: I—OWA).

Patient\ Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.063, 0.064〉	〈0.342, 0.343〉	〈0.174. 0.176〉	〈−0.056, 0.072〉	〈−0.167, 0.18〉
P2	〈−0.098, 0.152〉	〈−0.2, 0.224〉	〈0.02, 0.149〉	〈0.261, 0.262〉	〈−0.43, 0.44〉
P3	〈0.063, 0.065〉	〈0.342, 0.344〉	〈0.215, 0.217〉	〈−0.05, 0.07〉	〈−0.11, 0.13〉
P4	〈0.063, 0.064〉	〈0.342, 0.343〉	〈0.098, 0.15〉	〈−0.024, 0.1〉	〈−0.046, 0.08〉

Patient P₁ suffered from malaria fever with score (0.342); patient P₂ suffered from stomach problems with score (0.261); patient P₃ suffered from malaria fever with score (0.342); patient P₄ suffered from malaria fever with score (0.342).

Table 68. Membership and Non-membership degrees (Aggregation: q-ROFWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.204, 0.0〉	〈0.204, 0.0〉	〈0.204, 0.1〉	〈0.1, 0.4〉	〈0.1, 0.557〉
P2	〈0.089, 0.5〉	〈0.03, 0.6〉	〈0.089, 0.4〉	〈0.089, 0.0〉	〈0.089, 0.76〉
P3	〈0.17, 0.1〉	〈0.17, 0.1〉	〈0.17, 0.1〉	〈0.17, 0.4〉	〈0.1, 0.5〉
P4	〈0.114, 0.0〉	〈0.11, 0.0〉	〈0.114, 0.3〉	〈0.114, 0.4〉	〈0.11, 0.4〉

Table 68. Membership and Non-membership degrees (Aggregation: q-ROFWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.204, 0.0〉	〈0.204, 0.0〉	〈0.204, 0.1〉	〈0.1, 0.4〉	〈0.1, 0.557〉
P2	〈0.089, 0.5〉	〈0.03, 0.6〉	〈0.089, 0.4〉	〈0.089, 0.0〉	〈0.089, 0.76〉
P3	〈0.17, 0.1〉	〈0.17, 0.1〉	〈0.17, 0.1〉	〈0.17, 0.4〉	〈0.1, 0.5〉
P4	〈0.114, 0.0〉	〈0.11, 0.0〉	〈0.114, 0.3〉	〈0.114, 0.4〉	〈0.11, 0.4〉

Table 69. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: q-ROFWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.2048	0.2048	0.1051	−0.2911	−0.4232
P2	−0.3883	−0.5236	−0.3013	0.0898	−0.5364
P3	0.0709	0.0709	0.0709	−0.2199	−0.3781
P4	0.1143	0.1143	−0.1828	−0.2767	−0.2767

In patient P₁, the diseases viral fever and malaria fever showed the same relation value (0.2048), so, it was not obvious which disease P₁ was suffering from. Patient P₂ suffered from stomach problems with relation value (0.0898). In patient P₃, the diseases viral fever, malaria fever and typhoid fever showed the same relation value (0.0709), so, it was not obvious which disease P₃ was suffering from. In patient P₄, the diseases viral fever and malaria fever showed the same relation value (0.1143), so, it was not obvious which disease P₄ was suffering from.

Table 69. Final decision with ${\mathrm{R}\mathrm{V}}_1$ (Aggregation: q-ROFWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.2048	0.2048	0.1051	−0.2911	−0.4232
P2	−0.3883	−0.5236	−0.3013	0.0898	−0.5364
P3	0.0709	0.0709	0.0709	−0.2199	−0.3781
P4	0.1143	0.1143	−0.1828	−0.2767	−0.2767

In patient P₁, the diseases viral fever and malaria fever showed the same relation value (0.2048), so, it was not obvious which disease P₁ was suffering from. Patient P₂ suffered from stomach problems with relation value (0.0898). In patient P₃, the diseases viral fever, malaria fever and typhoid fever showed the same relation value (0.0709), so, it was not obvious which disease P₃ was suffering from. In patient P₄, the diseases viral fever and malaria fever showed the same relation value (0.1143), so, it was not obvious which disease P₄ was suffering from.

Table 70. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: q-ROFWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.1948	0.1948	0.0948	−0.3096	−0.4668
P2	−0.4194	−0.5791	−0.3198	0.0798	−0.6757
P3	0.0607	0.0607	0.0607	−0.2389	−0.4093
P4	0.1043	0.1043	−0.1955	−0.2953	−0.2953

In patient P₁, the diseases viral fever and malaria fever showed the same relation value (0.1948), so, it was not obvious which disease P₁ was suffering from. Patient P₂ suffered from stomach problems with relation value (0.0798). In patient P₃, the diseases viral fever, malaria fever and typhoid fever showed the same relation value (0.0607), so, it was not obvious which disease P₃ was suffering from. In patient P₄, the diseases viral fever and malaria fever showed the same relation value (0.1043), so, it was not obvious which disease P₄ was suffering from.

Table 70. Final decision with ${\mathrm{R}\mathrm{V}}_2$ (Aggregation: q-ROFWA).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.1948	0.1948	0.0948	−0.3096	−0.4668
P2	−0.4194	−0.5791	−0.3198	0.0798	−0.6757
P3	0.0607	0.0607	0.0607	−0.2389	−0.4093
P4	0.1043	0.1043	−0.1955	−0.2953	−0.2953

In patient P₁, the diseases viral fever and malaria fever showed the same relation value (0.1948), so, it was not obvious which disease P₁ was suffering from. Patient P₂ suffered from stomach problems with relation value (0.0798). In patient P₃, the diseases viral fever, malaria fever and typhoid fever showed the same relation value (0.0607), so, it was not obvious which disease P₃ was suffering from. In patient P₄, the diseases viral fever and malaria fever showed the same relation value (0.1043), so, it was not obvious which disease P₄ was suffering from.

Table 71. Score and Accuracy (Aggregation: q-ROFWA).

Patient\ Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.008, 0.008〉	〈0.008, 0.008〉	〈0.007, 0.009〉	〈−0.063, 0.065〉	〈−0.172, 0.174〉
P2	〈−0.124, 0.125〉	〈−0.21, 0.21〉	〈−0.063, 0.064〉	〈0.0, 0.0〉	〈−0.435, 0.436〉
P3	〈0.004, 0.06〉	〈0.004, 0.006〉	〈0.004, 0.006〉	〈−0.06, 0.07〉	〈−0.124, 0.126〉
P4	〈0.001, 0.001〉	〈0.001, 0.001〉	〈−0.025, 0.028〉	〈−0.062, 0.065〉	〈−0.062, 0.065〉

In patient P₁, the diseases viral fever and malaria fever showed the same score and accuracy (0.008, 0.008), so, it was not obvious which disease P₁ was suffering from. Patient P₂ suffered from stomach problems with score (0.0). In patient P₃, the diseases viral fever, malaria fever and typhoid fever showed the same score and accuracy (0.004, 0.06), so, it was not obvious which disease P₃ was suffering from. In patient P₄, the diseases viral fever and malaria fever showed the same score and accuracy (0.001, 0.001), so, it was not obvious which disease P₄ was suffering from.

Table 71. Score and Accuracy (Aggregation: q-ROFWA).

Patient\ Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	〈0.008, 0.008〉	〈0.008, 0.008〉	〈0.007, 0.009〉	〈−0.063, 0.065〉	〈−0.172, 0.174〉
P2	〈−0.124, 0.125〉	〈−0.21, 0.21〉	〈−0.063, 0.064〉	〈0.0, 0.0〉	〈−0.435, 0.436〉
P3	〈0.004, 0.06〉	〈0.004, 0.006〉	〈0.004, 0.006〉	〈−0.06, 0.07〉	〈−0.124, 0.126〉
P4	〈0.001, 0.001〉	〈0.001, 0.001〉	〈−0.025, 0.028〉	〈−0.062, 0.065〉	〈−0.062, 0.065〉

In patient P₁, the diseases viral fever and malaria fever showed the same score and accuracy (0.008, 0.008), so, it was not obvious which disease P₁ was suffering from. Patient P₂ suffered from stomach problems with score (0.0). In patient P₃, the diseases viral fever, malaria fever and typhoid fever showed the same score and accuracy (0.004, 0.06), so, it was not obvious which disease P₃ was suffering from. In patient P₄, the diseases viral fever and malaria fever showed the same score and accuracy (0.001, 0.001), so, it was not obvious which disease P₄ was suffering from.

3.3. Similarity Measures

Similarity measures are another way of decision-making in medical diagnosis. By applying Equation (22), (23) or (24), the final table of decision was calculated. According to Vlachos and Sergiadis (Equation (25)), the maximum value of the table indicated the dominant class (disease).

Table 72. Cosine Similarity.

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.9046	0.8832	0.8510	0.5033	0.4190
P2	0.5959	0.4400	0.7864	0.9808	0.6678
P3	0.8771	0.7381	0.9486	0.5559	0.4928
P4	0.9223	0.8911	0.8094	0.6545	0.6052

Patient P₁ suffered from viral fever with similarity (0.9046); patient P₂ suffered from stomach problems with similarity (0.9808); patient P₃ suffers from typhoid fever with similarity (0.9486); patient P₄ suffered from viral fever with similarity (0.9223).

,

Table 73. Peng Similarity.

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.7178	0.6713	0.6304	0.4774	0.4377
P2	0.5466	0.4823	0.5627	0.8027	0.5058
P3	0.6372	0.4919	0.6501	0.5789	0.4329
P4	0.6945	0.6210	0.5647	0.5461	0.3762

Patient P₁ suffered from viral fever with similarity (0.7178); patient P₂ suffered from stomach problems with similarity (0.8027); patient P₃ suffered from typhoid fever with similarity (0.6501); patientP₄ suffered from viral fever with similarity (0.6945).

,

Table 74. q-ROFC (q = 1).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.8385	0.8764	0.8147	0.5185	0.4348
P2	0.6536	0.4855	0.7838	0.9628	0.6570
P3	0.7648	0.6748	0.8307	0.5362	0.4756
P4	0.8750	0.8589	0.7705	0.6354	0.5769

Patient P₁ suffered from malaria fever with similarity (0.8764); patient P₂ suffered from stomach problems with similarity (0.9628); patient P₃ suffered from typhoid fever with similarity (0.8307); patient P₄ suffered from viral fever with similarity (0.8750).

,

Table 75. q-ROFC (q = 2).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.8736	0.9051	0.7954	0.6213	0.5109
P2	0.7680	0.6059	0.8175	0.9529	0.6572
P3	0.7656	0.6739	0.7715	0.6381	0.5486
P4	0.8830	0.7902	0.7568	0.7090	0.5364

Patient P₁ suffered from malaria fever with similarity (0.9051); patient P₂ suffered from stomach problems with similarity (0.9529); patient P₃ suffered from typhoid fever with similarity (0.7715); patient P₄ suffered from viral fever with similarity (0.8830).

and

Table 76. q-ROFC (q = 3).

Patient\Disease	Viral Fever	Malaria Fever	Typhoid Fever	Stomach Problems	Chest Problems
P1	0.9200	0.9269	0.8341	0.7777	0.6943
P2	0.8767	0.7426	0.8881	0.9500	0.7646
P3	0.8515	0.7552	0.7992	0.7825	0.6869
P4	0.9434	0.8200	0.8294	0.8521	0.6923

Patient P₁ suffered from malaria fever with similarity (0.9269); patient P₂ suffered from stomach problems with similarity (0.9500); patient P₃ suffered from viral fever with similarity (0.8515); patient P₄ suffered from viral fever with similarity (0.9434).

show the results similarity measures.

All the above results have been summarized in

Table 77. Final Table with medical diagnosis.

Intelligent Methods	Patients/Diseases
	${\mathbf{p}}_1$	${\mathbf{p}}_2$	${\mathbf{p}}_3$	${\mathbf{p}}_4$
1. Composite Fuzzy Relation
CFR1-RV1	Malaria fever	Stomach problems	Malaria fever	Malaria fever
CFR1-RV2	Malaria fever	Stomach problems	Malaria fever	Malaria fever
CFR1-Score and Accuracy	Malaria fever	Stomach problems	Malaria fever	Malaria fever
CFR2-RV1	Malaria fever	Typhoid fever	Stomach problems	Malaria fever
CFR2-RV2	Malaria fever	Typhoid fever	Stomach problems	Malaria fever
CFR2-Score and Accuracy	Malaria fever	Typhoid fever	Stomach problems	Malaria fever
2. Aggregation operators and q-ROFS
IFS (q = 1)
AM (RV1, RV2, Score and Accuracy)	Malaria fever	Stomach problems	Malaria fever	Malaria fever
HM (RV1, RV2, Score and Accuracy)	Malaria fever	Stomach problem	Malaria fever	Malaria fever
B-Z (RV1, RV2, Score and Accuracy)	Malaria fever	Stomach problems	Malaria fever	Malaria fever
I-OWA (RV1, RV2, Score and Accuracy)	Malaria fever	Stomach problems	Malaria fever	Malaria fever
q-ROFWA (RV1, RV2, Score and Accuracy)	Malaria fever	Stomach problems	Malaria fever	Malaria fever
PFS (q = 2)
AM (RV1, RV2, Score and Accuracy)	Malaria fever	Stomach problems	Malaria fever	Malaria fever
HM (RV1, RV2, Score and Accuracy)	Malaria fever	Stomach problems	Malaria fever	Malaria fever
B-Z (RV1, RV2, Score and Accuracy)	Malaria fever	Stomach problems	Malaria fever	Malaria fever
I-OWA (RV1, RV2, Score and Accuracy)	Malaria fever	Stomach problems	Malaria fever	Malaria fever
q-ROFWA (RV1, RV2, Score and Accuracy)	Viral fever/Malaria fever	Stomach problems	Typhoid fever	Viral fever/Malaria fever
FFS (q = 3)
AM (RV1, RV2, Score and Accuracy)	Malaria fever	Stomach problems	Malaria fever	Malaria fever
HM (RV1, RV2, Score and Accuracy)	Malaria fever	Stomach problems	Malaria fever	Malaria fever
B-Z (RV1, RV2, Score and Accuracy)	Malaria fever	Stomach problems	Malaria fever	Malaria fever
I-OWA (RV1, RV2, Score and Accuracy)	Malaria fever	Stomach problems	Malaria fever	Malaria fever
q-ROFWA (RV1, RV2, Score and Accuracy)	Viral fever/Malaria fever	Stomach problems	Viral fever/Malaria fever/Typhoid fever	Viral fever/Malaria fever
3. Similarity measure
CS (IFS)	Viral fever	Stomach problems	Typhoid fever	Viral fever
Peng similarity (S10)	Viral fever	Stomach problems	Typhoid fever	Viral fever
q-ROFC (q = 1)	Malaria fever	Stomach problems	Typhoid fever	Viral fever
q-ROFC (q = 2)	Malaria fever	Stomach problems	Typhoid fever	Viral fever
q-ROFC (q = 3)	Malaria fever	Stomach problems	Viral fever	Viral fever

.

4. Discussion

The results were derived from the proposed intelligent methods. All techniques presented were used for decision-making in medical diagnosis. In this study, we used three ways that helped to produce a final result. Using composite fuzzy relation 1 it was concluded that: ${\mathrm{p}}_1$ was suffering from malaria fever, ${\mathrm{p}}_2$ was suffering from stomach problems, ${\mathrm{p}}_3$ was suffering from malaria fever, and ${\mathrm{p}}_4$ was suffering from malaria fever. However, using composite fuzzy relation 2 it was concluded that: ${\mathrm{p}}_1$ was suffering from malaria fever, ${\mathrm{p}}_2$ was suffering from typhoid fever, ${\mathrm{p}}_3$ was suffering from stomach problems, and ${\mathrm{p}}_4$ was suffering from malaria fever. With regard to the second way, the results and procedure were complicated. Based on the previous studies that used Table 1 and Table 2 as data, it was mentioned that the majority of results share the same outcomes.

Table 78. Results from former works.

		${\mathbf{p}}_1$	${\mathbf{p}}_2$	${\mathbf{p}}_3$	${\mathbf{p}}_4$
q-ROFSs and Sanchez’s Method
[4,10,11]	q = 1	Malaria fever	Stomach problems	Malaria fever	Malaria fever
[4,5]	q = 2	Malaria fever	Stomach problems	Malaria fever	Malaria fever
[4]	q = 3	Malaria fever	Stomach problems	Malaria fever	Malaria fever
Distances
[11]	Hamming/Euclidean	Malaria fever	Stomach problems	Typhoid fever	Viral fever
Similarity Measures
[23]	$\tilde{\mathrm{S}}$	Malaria fever	Stomach problems	Typhoid fever	Viral fever
[23]	$\widehat{\mathrm{S}}$	Viral fever	Stomach problems	Typhoid fever	Viral fever
Divergence Measures
[17]	PIFDM	Viral fever	Stomach problems	Typhoid fever	Viral fever
[17]	${\mathrm{D}}_{\mathrm{W}\mathrm{Y}\left(\mathrm{a}\right)}\left(\mathrm{A}\mathrm{B}\right)$	Malaria fever	Stomach problems	Typhoid fever	Viral fever
[18]	PFSDM	Viral fever	Stomach problems	Typhoid fever	Viral fever
[18]	Xiao’smethod	Malaria fever	Stomach problems	Typhoid fever	Viral fever

presents the former works that used the same data (Table 1 and Table 2).

In previous studies [4,5,10,11] patients ${\mathrm{p}}_1,$ ${\mathrm{p}}_3,\text{and}{\mathrm{p}}_4$ suffered from malaria fever while patient ${\mathrm{p}}_2$ suffered from stomach problems. Also in these studies, the same methodology was used to derive the results, with the difference being that in the current study the data combination was used so that there was more than one expert’s opinion. In IFS (q = 1), the aggregation operators arithmetic mean, harmonic mean, Bellaman/Zadeh, I-OWA, and q-ROFWA brought the same results as the previous studies. In PFS (q = 2), the aggregation operators arithmetic mean, harmonic mean, Bellaman/Zadeh, and I-OWA had the same results, but the operator q-ROFWA brought different results. Similarly, the FFS (q = 3), the aggregation operators arithmetic mean, harmonic mean, Bellaman/Zadeh and I—OWA showed the same results, but the operator q-ROFWA showed different results. If there is more than one maximum value, it is not clear which disease is more dominant. Therefore, the operator q-ROFWA seemed to add more ambiguity to the data in order to differentiate them. Another point worth noting is that the values of the results decreased as q increased, and the reason for this is that more ambiguity was introduced into the system as q increased [4]. Lastly, there were the similarity measures for making a medical decision. The results were compared with various methods [11,17,18,23]. There are some extra methods beyond similarity measures, such as distance and divergence measures. These three methods are interrelated. Three similarity measures were used. While applying the cosine and the Peng similarity it was observed that they shared the same results: ${\mathrm{p}}_1$ was suffering from viral fever, ${\mathrm{p}}_2$ was suffering from stomach problems, ${\mathrm{p}}_3$ was suffering from typhoid fever, and ${\mathrm{p}}_4$ was suffering from viral fever. In former works [17,18,23] a likeness can be observed. However, in some cases, results were different because there were other similarity/divergence measures such as $\tilde{\mathrm{S}}$-measure, ${\mathrm{D}}_{\mathrm{W}\mathrm{Y}\left(\mathrm{a}\right)}\left(\mathrm{A}\mathrm{B}\right)$ and Xiao’s method that changed the results. In the last case of similarity measures (q-ROFC) it was noticed that there were some different results due to the introduction of the degree of indeterminacy $\mathsf{\pi }$ which included the uncertainty of the fuzzy sets. Regarding q = 1, ${\mathrm{p}}_1$ was suffering from malaria fever, ${\mathrm{p}}_2$ was suffering from stomach problems, ${\mathrm{p}}_3$ was suffering from typhoid fever, and ${\mathrm{p}}_4$ was suffering from viral fever. In former works [17,23], the measures of PIFDM distance and Frank t-norms referred to IFSs (q = 1) and two versions of results emerged. The first version conformed with the results from q-ROFC (q = 1) and the second version inclined. Concerning q = 2, ${\mathrm{p}}_1$ was suffering from malaria fever, ${\mathrm{p}}_2$ was suffering from stomach problems, ${\mathrm{p}}_3$ was suffering from typhoid fever, and ${\mathrm{p}}_4$ was suffering from viral fever. In former work [18], the measure of PFSDM distance referred to PFSs (q = 2) and two opinions of the results emerged. The first version conformed with the results from q-ROFC (q = 2) and the second version inclined. As far as q = 3, ${\mathrm{p}}_1$ was suffering from malaria fever, ${\mathrm{p}}_2$ was suffering from stomach problems, ${\mathrm{p}}_3$ was suffering from viral fever, and ${\mathrm{p}}_4$ was suffering from viral fever. There was a differentiation in ${\mathrm{p}}_3$.

5. Conclusions

The decision-making in medicine and the patient’s classification of various diseases depends on the expert’s interpretation according to symptoms and the medical specialist’s experience. Because of the difficulty of considering all of the accurate measurements and symptoms, experts often struggle to make a diagnosis due to imprecise knowledge which causes vagueness and uncertainty in the diagnosis procedure. For handling imprecise knowledge, fuzzy logic is often applied. Fuzzy logic is an important tool of artificial intelligence that mathematizes human language while dominating environments characterized by ambiguity, lack of knowledge, and uncertainty. The novelty and contribution of this work relied on the combination of various techniques for intelligent medical diagnosis reasoning. The aim of this paper was to assess the contribution of aggregation operators in q-ROFSs and to apply some extra similarity measures like Peng similarity. In this study, the patient’s medical status was represented as q-rung orthopair fuzzy values. The applied methods were as follows: composite fuzzy relation with min-max-min and max-average-min-average using different relation value types, aggregation operators for medical examination, and patient’s history based on q-ROFWA, I-OWA, Bellman-Zadeh, Harmonic Mean and Arithmetic Mean, similarity measures based on a cosine measure, and the Peng measure and q-ROFC measure. The results varied and it was uncertain which disease every patient was suffering from. This is due to subjective medical knowledge and, therefore, it was proposed to modify this knowledge so that the result of the diagnosis is acceptable as shown in the flowchart (Figure 2).

Of course, not all possible ways of making a medical diagnosis with fuzzy logic were studied above. There are several measures of similarity, and several aggregation operators and the q-rung can be extended more. Additionally, the composite fuzzy relation (max-min, min-max) cannot be extended to any set that has more than three components such as picture fuzzy sets. Future work will include fuzzy deep learning and providing more degrees of freedom for optimum handling of medical uncertainty. Moreover, a bigger and more realistic dataset will enrich the medical knowledge and, thus, the relation between symptoms and diseases will be more accurate. In addition, other effective factors in diagnosis are suggested such as sex, age, physical conditions, etc., for accurate decisions. In a disease diagnosis process, another future approach is the fuzzy cognitive map model designed to distinguish a disease properly from other diseases with the same symptoms. The proposed method can be improved further using Interval Type 2 Fuzzy Sets or Z-number to better represent uncertainty enhancing diagnosis accuracy. Regarding aggregation, different types of operators need to be explored in a fuzzy environment, and more experiments are necessary to find the most accurate method for medical diagnosis.