Submit to Mathematics Review for Mathematics Propose a Special Issue

Journal Browser

Fuzzy Sets, Fuzzy Logic and Their Applications

Special Issue Editors
Special Issue Information
Keywords
Published Papers

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Fuzzy Sets, Systems and Decision Making".

Deadline for manuscript submissions: closed (31 December 2019) | Viewed by 66888

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special issue Fuzzy Sets, Fuzzy Logic and Their Applications book cover image

Share This Special Issue

Special Issue Editor

Prof. Dr. Michael Voskoglou

E-Mail Website
Guest Editor

Graduate Technological Educational Institute (T.E.I.) of Western Greece, School of Technological Applications, 263 34 Patras, Greece
Interests: fuzzy sets and logic; Markov chains; abstract and linear algebra; artificial intelligence; mathematics education
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

A few years ago, probability theory was a unique tool in hands of the experts dealing with situations of uncertainty appearing in problems of science and in everyday life. However, nowadays, with the development of fuzzy set theory—introduced by Zadeh in 1965—and the extension of fuzzy logic, the situation has changed. In fact, these new mathematical tools provided scientists with the opportunity to model under conditions that are vague or not precisely defined, thus succeeding in mathematically solving problems whose statements are expressed in our natural language. As a result, the spectrum of application has been rapidly extended, covering all of the physical sciences, economics and management, expert systems like financial planners, diagnostic, meteorological, information retrieval, control systems, etc., industry, robotics, decision making, programming, medicine, biology, humanities, education and almost all the other sectors of the human activity, including human reasoning itself. The first major commercial application of fuzzy logic was in cement kiln control (Zadeh, 1983), followed by a navigation system for automatic cars, a fuzzy controller for the automatic operation of trains, laboratory level controllers, controllers for robot vision, graphics, controllers for automated police sketchers and many others. It should be mentioned that fuzzy mathematics has been also significantly developed on the theoretical level, providing important insights even to branches of the classical mathematics, like algebra, analysis, geometry, etc.

The target of the present Special Issue of the MDPI journal Mathematics is to provide the experts in the field (academics, researchers, practitioners, etc.) the opportunity to present recent theoretical advances on fuzzy sets and fuzzy logic and of their extension/generalization (e.g. intuitionistic fuzzy logic, neutrosophic sets, etc.) and their applications to all fields of human activity.

Prof. Michael Voskoglou
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

Fuzzy Sets and their Generalizations
Fuzzy Logic
Defuzzification Techniques
Fuzzy Numbers
Uncertainty in Fuzzy Environments

Published Papers (20 papers)

Download All Papers

Research

Jump to: Review

17 pages, 312 KiB

Open AccessArticle

Separation Axioms of Interval-Valued Fuzzy Soft Topology via Quasi-Neighborhood Structure

by Mabruka Ali, Adem Kılıçman and Azadeh Zahedi Khameneh

Mathematics 2020, 8(2), 178; https://doi.org/10.3390/math8020178 - 02 Feb 2020

Cited by 5 | Viewed by 2298

Abstract

In this study, we present the concept of the interval-valued fuzzy soft point and then introduce the notions of its neighborhood and quasi-neighborhood in interval-valued fuzzy soft topological spaces. Separation axioms in an interval-valued fuzzy soft topology, so-called q-

T_{i}

for [...] Read more.

T_{i}

for

i = 0, 1, 2, 3, 4

, are introduced, and some of their basic properties are also studied. Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)

20 pages, 2415 KiB

Open AccessArticle

A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis

by Qianli Zhou, Hongming Mo and Yong Deng

Mathematics 2020, 8(1), 142; https://doi.org/10.3390/math8010142 - 20 Jan 2020

Cited by 101 | Viewed by 5018

Abstract

As the extension of the fuzzy sets (FSs) theory, the intuitionistic fuzzy sets (IFSs) play an important role in handling the uncertainty under the uncertain environments. The Pythagoreanfuzzy sets (PFSs) proposed by Yager in 2013 can deal with more uncertain situations than intuitionistic fuzzy sets because of its larger range of describing the membership grades. How to measure the distance of Pythagorean fuzzy sets is still an open issue. Jensen–Shannon divergence is a useful distance measure in the probability distribution space. In order to efficiently deal with uncertainty in practical applications, this paper proposes a new divergence measure of Pythagorean fuzzy sets, which is based on the belief function in Dempster–Shafer evidence theory, and is called PFSDM distance. It describes the Pythagorean fuzzy sets in the form of basic probability assignments (BPAs) and calculates the divergence of BPAs to get the divergence of PFSs, which is the step in establishing a link between the PFSs and BPAs. Since the proposed method combines the characters of belief function and divergence, it has a more powerful resolution than other existing methods. Additionally, an improved algorithm using PFSDM distance is proposed in medical diagnosis, which can avoid producing counter-intuitive results especially when a data conflict exists. The proposed method and the magnified algorithm are both demonstrated to be rational and practical in applications. Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)

► Show Figures

Figure 1

23 pages, 1638 KiB

Open AccessArticle

Picture Fuzzy Interaction Partitioned Heronian Aggregation Operators for Hotel Selection

by Suizhi Luo and Lining Xing

Mathematics 2020, 8(1), 3; https://doi.org/10.3390/math8010003 - 18 Dec 2019

Cited by 14 | Viewed by 1898

Abstract

Picture fuzzy numbers (PFNs), as the generalization of fuzzy sets, are good at fully expressing decision makers’ opinions with four membership degrees. Since aggregation operators are simple but powerful tools, this study aims to explore some aggregation operators with PFNs to solve practical decision-making problems. First, new operational rules, the interaction operations of PFNs, are defined to overcome the drawbacks of existing operations. Considering that interrelationships may exist only in part of criteria, rather than all of the criteria in reality, the partitioned Heronian aggregation operator is modified with PFNs to deal with this condition. Then, desirable properties are proved and several special cases are discussed. New decision-making methods with these presented aggregation operators are suggested to process hotel selection issues. Last, their practicability and merits are certified by sensitivity analyses and comparison analyses with other existing approaches. The results indicate that our methods are feasible to address such situations where criteria interact in the same part, but are independent from each other at different parts. Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)

► Show Figures

Figure 1

20 pages, 4598 KiB

Open AccessArticle

A Fuzzy Collaborative Approach for Evaluating the Suitability of a Smart Health Practice

by Tin-Chih Toly Chen, Yu-Cheng Wang, Yu-Cheng Lin, Hsin-Chieh Wu and Hai-Fen Lin

Mathematics 2019, 7(12), 1180; https://doi.org/10.3390/math7121180 - 03 Dec 2019

Cited by 10 | Viewed by 1980

Abstract

A fuzzy collaborative approach is proposed in this study to assess the suitability of a smart health practice, which is a challenging task, as the participating decision makers may not reach a consensus. In the fuzzy collaborative approach, each decision maker first applies the alpha-cut operations method to derive the fuzzy weights of the criteria. Then, fuzzy intersection is applied to aggregate the fuzzy weights derived by all decision makers to measure the prior consensus among them. The fuzzy intersection results are then presented to the decision makers so that they can subjectively modify the pairwise comparison results to bring them closer to the fuzzy intersection results. Thereafter, the consensus among decision makers is again measured. The collaboration process will stop when no more modifications are made by any decision maker. Finally, the fuzzy weighted mean-centroid defuzzification method is applied to assess the suitability of a smart health practice. The fuzzy collaborative approach and some existing methods have been applied to assess the suitabilities of eleven smart health practices for a comparison. Among the compared practices, only the fuzzy collaborative approach could guarantee the existence of a full consensus among decision makers after the collaboration process, i.e., that the assessment results were acceptable to all decision makers. Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)

► Show Figures

Figure 1

7 pages, 241 KiB

Open AccessArticle

On ω-Limit Sets of Zadeh’s Extension of Nonautonomous Discrete Systems on an Interval

by Guangwang Su and Taixiang Sun

Mathematics 2019, 7(11), 1116; https://doi.org/10.3390/math7111116 - 15 Nov 2019

Viewed by 1586

Abstract

Let

I = [0, 1]

and

f_{n}

be a sequence of continuous self-maps on I which converge uniformly to a self-map f on I. Denote by

F (I)

the set of fuzzy numbers on I, [...] Read more.

Let

I = [0, 1]

and

f_{n}

be a sequence of continuous self-maps on I which converge uniformly to a self-map f on I. Denote by

F (I)

the set of fuzzy numbers on I, and denote by

(F (I), \hat{f})

and

(F (I), {\hat{f}}_{n})

the Zadeh

^{'}

s extensions of

(I, f)

and

(I, f_{n})

, respectively. In this paper, we study the

ω

-limit sets of

(F (I), {\hat{f}}_{n})

and show that, if all periodic points of f are fixed points, then

ω (A, {\hat{f}}_{n}) \subset F (\hat{f})

for any

A \in F (I)

, where

ω (A, {\hat{f}}_{n})

is the

ω

-limit set of A under

(F (I), {\hat{f}}_{n})

and

F (\hat{f}) = {A \in F (I) : \hat{f} (A) = A}

. Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)

18 pages, 297 KiB

Open AccessArticle

Bipolar Fuzzy Relations

by Jeong-Gon Lee and Kul Hur

Mathematics 2019, 7(11), 1044; https://doi.org/10.3390/math7111044 - 03 Nov 2019

Cited by 18 | Viewed by 4141

Abstract

We introduce the concepts of a bipolar fuzzy reflexive, symmetric, and transitive relation. We study bipolar fuzzy analogues of many results concerning relationships between ordinary reflexive, symmetric, and transitive relations. Next, we define the concepts of a bipolar fuzzy equivalence class and a bipolar fuzzy partition, and we prove that the set of all bipolar fuzzy equivalence classes is a bipolar fuzzy partition and that the bipolar fuzzy equivalence relation is induced by a bipolar fuzzy partition. Finally, we define an

(a, b)

-level set of a bipolar fuzzy relation and investigate some relationships between bipolar fuzzy relations and their

(a, b)

-level sets. Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)

19 pages, 1312 KiB

Open AccessArticle

Quantitative Analysis of Key Performance Indicators of Green Supply Chain in FMCG Industries Using Non-Linear Fuzzy Method

by Hamed Nozari, Esmaeil Najafi, Mohammad Fallah and Farhad Hosseinzadeh Lotfi

Mathematics 2019, 7(11), 1020; https://doi.org/10.3390/math7111020 - 27 Oct 2019

Cited by 22 | Viewed by 6171

Abstract

Nowadays, along with increasing companies’ activities, one of the main environmental protective tools is green supply chain management (GSCM). Since fast-moving consumer goods (FMCG) companies are manufacturing materials that usually require special warehousing as well as different distribution systems, and since companies of food products tend to fall into this area, the safety of their manufactured materials is a vital global challenge. For this reason, organizations in addition to governments have realized the importance of the green supply chain in these industries. Therefore, the present study examines the key performance indicators (KPIs) of the green supply chain in the FMCG industry. There are several performance indicators for the green supply chain. In this study, the KPIs were extracted based on the literatures as well as the opinions of experts through which key indicators in FMCG industries were identified. Using the fuzzy decision -making trial and evaluation laboratory (DEMATEL) method, the relationships and interactions of these key indices were determined. Moreover, a fuzzy nonlinear mathematical modeling was used to investigate the significance of these indicators. It is revealed that the organizational environmental management factor has the highest priority. Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)

► Show Figures

Figure 1

16 pages, 270 KiB

Open AccessArticle

Degrees of L-Continuity for Mappings between L-Topological Spaces

by Zhenyu Xiu and Qinghua Li

Mathematics 2019, 7(11), 1013; https://doi.org/10.3390/math7111013 - 24 Oct 2019

Cited by 36 | Viewed by 1782

Abstract

By means of the residual implication on a frame L, a degree approach to L-continuity and L-closedness for mappings between L-cotopological spaces are defined and their properties are investigated systematically. In addition, in the situation of L-topological spaces, degrees of L-continuity and of L-openness for mappings are proposed and their connections are studied. Moreover, if L is a frame with an order-reversing involution

^{'}

, where

b^{'} = b \to ⊥

for

b \in L

, then degrees of L-continuity for mappings between L-cotopological spaces and degrees of L-continuity for mappings between L-topological spaces are equivalent. Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)

18 pages, 316 KiB

Open AccessArticle

Fuzzy Counterparts of Fischer Diagonal Condition in ⊤-Convergence Spaces

by Qiu Jin, Lingqiang Li and Jing Jiang

Mathematics 2019, 7(8), 685; https://doi.org/10.3390/math7080685 - 31 Jul 2019

Cited by 1 | Viewed by 1918

Abstract

Fischer diagonal condition plays an important role in convergence space since it precisely ensures a convergence space to be a topological space. Generally, Fischer diagonal condition can be represented equivalently both by Kowalsky compression operator and Gähler compression operator. ⊤-convergence spaces are fundamental fuzzy extensions of convergence spaces. Quite recently, by extending Gähler compression operator to fuzzy case, Fang and Yue proposed a fuzzy counterpart of Fischer diagonal condition, and proved that ⊤-convergence space with their Fischer diagonal condition just characterizes strong L-topology—a type of fuzzy topology. In this paper, by extending the Kowalsky compression operator, we present a fuzzy counterpart of Fischer diagonal condition, and verify that a ⊤-convergence space with our Fischer diagonal condition precisely characterizes topological generated L-topology—a type of fuzzy topology. Hence, although the crisp Fischer diagonal conditions based on the Kowalsky compression operator and the on Gähler compression operator are equivalent, their fuzzy counterparts are not equivalent since they describe different types of fuzzy topologies. This indicates that the fuzzy topology (convergence) is more complex and varied than the crisp topology (convergence). Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)

► Show Figures

Figure 1

31 pages, 3574 KiB

Open AccessArticle

An Interactive Data-Driven (Dynamic) Multiple Attribute Decision Making Model via Interval Type-2 Fuzzy Functions

by Adil Baykasoğlu and İlker Gölcük

Mathematics 2019, 7(7), 584; https://doi.org/10.3390/math7070584 - 30 Jun 2019

Cited by 6 | Viewed by 3467

Abstract

A new multiple attribute decision making (MADM) model was proposed in this paper in order to cope with the temporal performance of alternatives during different time periods. Although dynamic MADM problems are enjoying a more visible position in the literature, majority of the applications deal with combining past and present data by means of aggregation operators. There is a research gap in developing data-driven methodologies to capture the patterns and trends in the historical data. In parallel with the fact that style of decision making evolving from intuition-based to data-driven, the present study proposes a new interval type-2 fuzzy (IT2F) functions model in order to predict current performance of alternatives based on the historical decision matrices. As the availability of accurate historical data with desired quality cannot always be obtained and the data usually involves imprecision and uncertainty, predictions regarding the performance of alternatives are modeled as IT2F sets. These estimated outputs are transformed into interpretable forms by utilizing the vocabulary matching procedures. Then the interactive procedures are employed to allow decision makers to modify the predicted decision matrix based on their perceptions and subjective judgments. Finally, ranking of alternatives are performed based on past and current performance scores. Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)

► Show Figures

Graphical abstract

12 pages, 763 KiB

Open AccessArticle

Distance Measures between the Interval-Valued Complex Fuzzy Sets

by Songsong Dai, Lvqing Bi and Bo Hu

Mathematics 2019, 7(6), 549; https://doi.org/10.3390/math7060549 - 16 Jun 2019

Cited by 53 | Viewed by 3851

Abstract

Complex fuzzy set (CFS) is a recent development in the field of fuzzy set (FS) theory. The significance of CFS lies in the fact that CFS assigned membership grades from a unit circle in the complex plane, i.e., in the form of a [...] Read more.

[0, 1]

interval. The interval-valued complex fuzzy set (IVCFS) is one of the extensions of the CFS in which the amplitude term is extended from the real numbers to the interval-valued numbers. The novelty of IVCFS lies in its larger range comparative to CFS. We often use fuzzy distance measures to solve some problems in our daily life. Hence, this paper develops some series of distance measures between IVCFSs by using Hamming and Euclidean metrics. The boundaries of these distance measures for IVCFSs are obtained. Finally, we study two geometric properties include rotational invariance and reflectional invariance of these distance measures. Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)

► Show Figures

Figure 1

18 pages, 1014 KiB

Open AccessArticle

New Concepts of Picture Fuzzy Graphs with Application

by Cen Zuo, Anita Pal and Arindam Dey

Mathematics 2019, 7(5), 470; https://doi.org/10.3390/math7050470 - 24 May 2019

Cited by 63 | Viewed by 6774

Abstract

The picture fuzzy set is an efficient mathematical model to deal with uncertain real life problems, in which a intuitionistic fuzzy set may fail to reveal satisfactory results. Picture fuzzy set is an extension of the classical fuzzy set and intuitionistic fuzzy set. It can work very efficiently in uncertain scenarios which involve more answers to these type: yes, no, abstain and refusal. In this paper, we introduce the idea of the picture fuzzy graph based on the picture fuzzy relation. Some types of picture fuzzy graph such as a regular picture fuzzy graph, strong picture fuzzy graph, complete picture fuzzy graph, and complement picture fuzzy graph are introduced and some properties are also described. The idea of an isomorphic picture fuzzy graph is also introduced in this paper. We also define six operations such as Cartesian product, composition, join, direct product, lexicographic and strong product on picture fuzzy graph. Finally, we describe the utility of the picture fuzzy graph and its application in a social network. Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)

► Show Figures

Figure 1

10 pages, 237 KiB

Open AccessArticle

Counterintuitive Test Problems for Distance-Based Similarity Measures Between Intuitionistic Fuzzy Sets

by Hui-Chin Tang and Shen-Tai Yang

Mathematics 2019, 7(5), 437; https://doi.org/10.3390/math7050437 - 17 May 2019

Cited by 3 | Viewed by 1801

Abstract

This paper analyzes the counterintuitive behaviors of adopted twelve distance-based similarity measures between intuitionistic fuzzy sets. Among these distance-based similarity measures, the largest number of components of the distance in the similarity measure is four. We propose six general counterintuitive test problems to analyze their counterintuitive behaviors. The results indicate that all the distance-based similarity measures have some counterintuitive test problems. Furthermore, for the largest number of components of the distance-based similarity measure, four types of counterintuitive examples exist. Therefore, the counterintuitive behaviors are inevitable for the distance-based similarity measures between intuitionistic fuzzy sets. Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)

14 pages, 310 KiB

Open AccessArticle

p-Regularity and p-Regular Modification in ⊤-Convergence Spaces

by Qiu Jin, Lingqiang Li and Guangming Lang

Mathematics 2019, 7(4), 370; https://doi.org/10.3390/math7040370 - 24 Apr 2019

Cited by 27 | Viewed by 2211

Abstract

Fuzzy convergence spaces are extensions of convergence spaces. ⊤-convergence spaces are important fuzzy convergence spaces. In this paper, p-regularity (a relative regularity) in ⊤-convergence spaces is discussed by two equivalent approaches. In addition, lower and upper p-regular modifications in ⊤-convergence spaces are further investigated and studied. Particularly, it is shown that lower (resp., upper) p-regular modification and final (resp., initial) structures have good compatibility. Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)

18 pages, 313 KiB

Open AccessArticle

On (α,β)-US Sets in BCK/BCI-Algebras

by Chiranjibe Jana and Madhumangal Pal

Mathematics 2019, 7(3), 252; https://doi.org/10.3390/math7030252 - 11 Mar 2019

Cited by 7 | Viewed by 1980

Abstract

Molodtsov originated soft set theory, which followed a general mathematical framework for handling uncertainties, in which we encounter the data by affixing the parameterized factor during the information analysis. The aim of this paper is to establish a bridge to connect a soft [...] Read more.

B C K / B C I

-algebras. Firstly, we introduce the notion of the

(α, β)

-Union-Soft (

(α, β)

-US) set, with some supporting examples. Then, we discuss the soft

B C K / B C I

-algebras, which are called

(α, β)

-US algebras,

(α, β)

-US ideals,

(α, β)

-US closed ideals, and

(α, β)

-US commutative ideals. In particular, some related properties and relationships of the above algebraic structures are investigated. We also provide the condition of an

(α, β)

-US ideal to be an

(α, β)

-US closed ideal. Some conditions for a Union-Soft (US) ideal to be a US commutative ideal are given by means of

(α, β)

-unions. Moreover, several characterization theorems of (closed) US ideals and US commutative ideals are given in terms of

(α, β)

-unions. Finally, the extension property for an

(α, β)

-US commutative ideal is established. Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)

10 pages, 237 KiB

Open AccessArticle

The “Generator” of Int-Soft Filters on Residuated Lattices

by Huarong Zhang and Minxia Luo

Mathematics 2019, 7(3), 236; https://doi.org/10.3390/math7030236 - 06 Mar 2019

Cited by 1 | Viewed by 1785

Abstract

In this paper, we give the “generator” of int-soft filters and propose the notion of t-int-soft filters on residuated lattices. We study the properties of t-int-soft filters and obtain some commonalities (e.g., the extension property, quotient characteristics, and a triple of equivalent characteristics). We also use involution-int-soft filters as an example and show some basic properties of involution-int-soft filters. Finally, we investigate the relations among t-int-soft filters and give a simple method for judging their relations. Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)

18 pages, 305 KiB

Open AccessArticle

p-Topologicalness—A Relative Topologicalness in ⊤-Convergence Spaces

by Lingqiang Li

Mathematics 2019, 7(3), 228; https://doi.org/10.3390/math7030228 - 01 Mar 2019

Cited by 25 | Viewed by 1826

Abstract

In this paper, p-topologicalness (a relative topologicalness) in ⊤-convergence spaces are studied through two equivalent approaches. One approach generalizes the Fischer’s diagonal condition, the other approach extends the Gähler’s neighborhood condition. Then the relationships between p-topologicalness in ⊤-convergence spaces and p-topologicalness in stratified L-generalized convergence spaces are established. Furthermore, the lower and upper p-topological modifications in ⊤-convergence spaces are also defined and discussed. In particular, it is proved that the lower (resp., upper) p-topological modification behaves reasonably well relative to final (resp., initial) structures. Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)

15 pages, 2766 KiB

Open AccessEditor’s ChoiceArticle

A Partial-Consensus Posterior-Aggregation FAHP Method—Supplier Selection Problem as an Example

by Yu-Cheng Wang and Tin-Chih Toly Chen

Mathematics 2019, 7(2), 179; https://doi.org/10.3390/math7020179 - 15 Feb 2019

Cited by 37 | Viewed by 2956

Abstract

Existing fuzzy analytic hierarchy process (FAHP) methods usually aggregate the fuzzy pairwise comparison results produced by multiple decision-makers (DMs) rather than the fuzzy weights estimations. This is problematic because fuzzy pairwise comparison results are subject to uncertainty and lack consensus. To address this problem, a partial-consensus posterior-aggregation FAHP (PCPA-FAHP) approach is proposed in this study. The PCPA-FAHP approach seeks a partial consensus among most DMs instead of an overall consensus among all DMs, thereby increasing the possibility of reaching a consensus. Subsequently, the aggregation result is defuzzified using the prevalent center-of-gravity method. The PCPA-FAHP approach was applied to a supplier selection problem to validate its effectiveness. According to the experimental results, the PCPA-FAHP approach not only successfully found out the partial consensus among the DMs, but also shrunk the widths of the estimated fuzzy weights to enhance the precision of the FAHP analysis. Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)

► Show Figures

Figure 1

Review

Jump to: Research

22 pages, 2030 KiB

Open AccessReview

Fuzzy Logic and Its Uses in Finance: A Systematic Review Exploring Its Potential to Deal with Banking Crises

by Marc Sanchez-Roger, María Dolores Oliver-Alfonso and Carlos Sanchís-Pedregosa

Mathematics 2019, 7(11), 1091; https://doi.org/10.3390/math7111091 - 11 Nov 2019

Cited by 23 | Viewed by 7207

Abstract

The major success of fuzzy logic in the field of remote control opened the door to its application in many other fields, including finance. However, there has not been an updated and comprehensive literature review on the uses of fuzzy logic in the financial field. For that reason, this study attempts to critically examine fuzzy logic as an effective, useful method to be applied to financial research and, particularly, to the management of banking crises. The data sources were Web of Science and Scopus, followed by an assessment of the records according to pre-established criteria and an arrangement of the information in two main axes: financial markets and corporate finance. A major finding of this analysis is that fuzzy logic has not yet been used to address banking crises or as an alternative to ensure the resolvability of banks while minimizing the impact on the real economy. Therefore, we consider this article relevant for supervisory and regulatory bodies, as well as for banks and academic researchers, since it opens the door to several new research axes on banking crisis analyses using artificial intelligence techniques. Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)

► Show Figures

Figure 1

21 pages, 1751 KiB

Open AccessReview

Methods for Assessing Human–Machine Performance under Fuzzy Conditions

by Michael Gr. Voskoglou

Mathematics 2019, 7(3), 230; https://doi.org/10.3390/math7030230 - 01 Mar 2019

Cited by 18 | Viewed by 2870

Abstract

The assessment of a system’s performance is a very important task, enabling its designer/user to correct its weaknesses and make it more effective. Frequently, in practice, a system’s assessment is performed under fuzzy conditions, e.g., using qualitative instead of numerical grades, incomplete information about its function, etc. The present review summarizes the author’s research on building assessment models for use in a fuzzy environment. Those models include the measurement of a fuzzy system’s uncertainty, the application of the center of gravity defuzzification technique, the use of triangular fuzzy or grey numbers as assessment tools, and the application of the fuzzy relation equations. Examples are provided of assessing human (students and athletes) and machine (case-based reasoning systems in computers) capacities, illustrating our results. The outcomes of those examples are compared to the outcomes of the traditional methods of calculating the mean value of scores assigned to the system’s components (system’s mean performance) and of the grade point average index (quality performance) and useful conclusions are obtained concerning their advantages and disadvantages. The present review forms a new basis for further research on systems’ assessment in a fuzzy environment. Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Fuzzy Sets, Fuzzy Logic and Their Applications

Share This Special Issue

Special Issue Editor

Special Issue Information

Keywords

Published Papers (20 papers)

Research

Review

Further Information

Guidelines

MDPI Initiatives

Follow MDPI