Search Results (12)

Multi-criteria decision-making (MCDM) problems in complex evaluation systems are often characterized by high uncertainty in expert judgments and dynamic variations in indicator importance. Traditional analytic hierarchy process (AHP) and entropy-based weighting methods typically suffer from two inherent limitations: the inability to explicitly quantify expert hesitation and the rigidity of static weight assignment under evolving data distributions. To address these challenges, this paper proposes a dynamic hybrid weighting framework that integrates an interval-valued intuitionistic fuzzy analytic hierarchy process (IVIF-AHP) with an entropy-triggered correction mechanism. First, interval-valued intuitionistic fuzzy numbers are employed to simultaneously model membership, non-membership, and hesitation degrees in pairwise comparisons, enabling a more comprehensive representation of expert uncertainty. Second, an entropy-triggered dynamic fusion strategy is developed by jointly incorporating information entropy and coefficient of variation, allowing adaptive adjustment between subjective expert weights and objective data-driven weights. This mechanism effectively enhances sensitivity to high-dispersion criteria while preserving expert knowledge in low-variability indicators. The proposed framework is formulated in a hierarchical fuzzy decision structure and implemented through a fuzzy comprehensive evaluation process. Its feasibility and robustness are validated through a concrete case study on teaching effectiveness evaluation for a university engineering course, leveraging multi-source data. Comparative analysis demonstrates that the proposed approach effectively mitigates the weight rigidity and evaluation inflation observed in conventional methods. Furthermore, it improves diagnostic resolution and decision stability across different evaluation periods. The results indicate that the proposed entropy-triggered IVIF-AHP framework provides a mathematically sound and practically applicable solution for dynamic MCDM problems under uncertainty, with strong potential for extension to other complex evaluation and decision-support systems. Full article

As a non-associative connective in fuzzy logic, the analysis and research of overlap functions have been extended to many generalized cases, such as interval-valued and intuitionistic fuzzy overlap functions (IFOFs). However, overlap functions face challenges in the Pythagorean fuzzy (PF) environment. This paper first extends overlap functions to the PF domain by proposing PF overlap functions (PFOFs), discussing their representable forms, and providing a general construction method. It then introduces a new PF similarity measure which addresses issues in existing measures (e.g., the inability to measure the similarity of certain PF numbers) and demonstrates its effectiveness through comparisons with other methods, using several examples in fractional form. Based on the proposed PFOFs and their induced residual implication, new generalized PF rough sets (PFRSs) are constructed, which extend the PFRS models. The relevant properties of their approximation operators are explored, and they are generalized to the dual-domain case. Due to the introduction of hesitation in IF and PF sets, the approximate accuracy of classical rough sets is no longer applicable. Therefore, a new PFRS approximate accuracy is developed which generalizes the approximate accuracy of classical rough sets and remains applicable to the classical case. Finally, three multi-criteria decision-making (MCDM) algorithms based on PF information are proposed, and their effectiveness and rationality are validated through examples, making them more flexible for solving MCDM problems in the PF environment. Full article

In multi-attribute decision making (MADM), complex situations often arise where decision attributes are interval-valued hesitant fuzzy numbers (IVHFNs) and the attributes are interrelated. Traditional decision-making methods may be ineffective in handling such cases, highlighting the practical importance of seeking more effective approaches. Therefore, finding a more effective decision-making approach has important practical significance. By combining the theories of Archimedean S-norms and T-norms, we innovatively propose a multi-attribute decision-making method based on the generalized interval-valued hesitant fuzzy weighted Heronian mean (GIVHFWHM) operator to address the aforementioned issues. Initially, based on the operational laws of IVHFNs and the Heronian mean (HM) operator, we introduce the generalized interval-valued hesitant fuzzy Heronian mean (GIVHFHM) operator and the GIVHFWHM operator. We then examine properties of the GIVHFHM operator, including permutation invariance, idempotency, monotonicity, boundedness, and parameter symmetry. A multi-attribute decision-making model is constructed based on the GIVHFWHM operator. Finally, we validate the proposed model through numerical experiments in MADM. The results demonstrate that the new decision-making method, based on the GIVHFWHM operator, is feasible and effective in handling multi-attribute decision problems involving IVHFNs with interdependent attributes. This approach provides a novel perspective and method for solving MADM problems under interval-valued hesitant fuzzy conditions with interdependent attributes. It enriches the theoretical framework of multi-attribute hesitant decision models and expands the application of the Heronian mean operator within interval-valued hesitant fuzzy environments. This methodology assists decision makers in making more accurate decisions within complex decision-making contexts, enhancing both the scientific rigor and reliability of decision-making processes. Full article

The intuitionistic hesitant fuzzy set is a significant extension of the intuitionistic fuzzy set, specifically designed to address uncertain information in decision-making challenges. Aggregation operators play a fundamental role in combining intuitionistic hesitant fuzzy numbers into a unified component. This study aims to introduce two novel approaches. Firstly, we propose a three-way model for investors in the business domain, which utilizes interval-valued equivalence classes under the framework of intuitionistic hesitant fuzzy information. Secondly, we present a multiple-attribute decision-making (MADM) method using various aggregation operators for intuitionistic hesitant fuzzy sets (IHFSs). These operators include the IHF Aczel–Alsina average $\left(IHF{\mathcal{A}}_{\mathcal{A}}\mathrm{A}\right)$ operator, the IHF Aczel–Alsina weighted average $\left(IHF{\mathcal{A}}_{\mathcal{A}}W{A}_{\mathsf{ϣ}}\right)$ operator, and the IHF Aczel–Alsina ordered weighted average $\left(IHF{\mathcal{A}}_{\mathcal{A}}OW{A}_{\mathsf{ϣ}}\right)$ operator and the IHF Aczel–Alsina hybrid average $\left(IHF{\mathcal{A}}_{\mathcal{A}}H{A}_{\mathsf{ϣ}}\right)$ operators. We demonstrate the properties of idempotency, boundedness, and monotonicity for these newly established aggregation operators. Additionally, we provide a detailed technique for three-way decision-making using intuitionistic hesitant fuzzy Aczel–Alsina aggregation operators. Furthermore, we present a numerical case analysis to illustrate the pertinency and authority of the esteblished model for investment in business. In conclusion, we highlight that the developed approach is highly suitable for investment selection policies, and we anticipate its extension to other fuzzy information domains. Full article

Hesitant fuzzy evaluation strategy related to the interval-valued membership and nonmembership degrees should be an appropriate choice due to the lack of experience, ability and knowledge of some decision experts. In addition, it is important to reasonably model the interrelationship of these experts. In this work, firstly, the generalized interval-valued q-rung orthopair hesitant fuzzy sets (GIVqROHFSs) are defined, and some operational rules with respect to GIVqROF numbers are discussed. Secondly, two types of operators, which are denoted as GIVqROHFCA and GIVqROHFCGM, are developed. Thirdly, the desired properties and relationships of two operators are studied. Furthermore, a new multiple attributes group decision making (MAGDM) approach is proposed. Finally, three experiments are completed to illustrate the rationality of the developed method and the monotonicity of this approach concerning the parameter in the GIVqROHFCGM operator and the GIVqROHFCA operator which meets symmetrical characteristics, and shows the superiority and reliability of this new method in solving the GIVqROHF problems. The main advantages of this work include three points: (1) extending hesitant fuzzy sets to the interval-valued q-rung orthopair fuzzy case and proposing two types of aggregation operators for the GIVqROHF information; (2) considering the interaction among decision makers and among attributes in decision problems, and dealing with this interrelationship by fuzzy measure; (3) introducing the new decision method for the GIVqROHF environment and enriching the mathematical tools to solve multiple attributes decision-making problems. Full article

Global economic integration drives the development of dynamic competition. In a dynamic competitive environment, the ever-changing customer demands and technology directly affect the leadership of the core competence of enterprises. Therefore, assessing the performance of enterprises in a timely manner is necessary to adjust business activities and completely adapt to new changes. Enterprise diagnosis is a scientific tool for judging the development status of enterprises, and building a scientific and rational index system is the key to enterprise diagnosis. Considering the large number of enterprise diagnostic indicators and the high similarity among indicators, this study proposes a selection method for enterprise diagnostic indicators based on interval-valued hesitant fuzzy clustering by comparing the existing indicator systems. First, enterprise organizations are considered as the starting point. Through the key analysis of relevant indicators of domestic and foreign enterprise diagnosis, enterprise diagnosis candidate indicators are constructed from three aspects, namely enterprise performance, employee health, and social benefit. In view of the ambiguity and inconsistency of expert judgment, this study proposes an interval-valued hesitant fuzzy set based on the characteristics of hesitant fuzzy sets and interval-valued evaluation. For improving the interval-valued hesitant fuzzy entropy function, an interval-valued hesitant fuzzy similarity measurement formula considering information features is designed to avoid the problem of data length and improve the degree of identification among indicators. Then, the similarity, equivalence, and truncation matrices are constructed, and the interval-valued hesitant fuzzy clustering method is used to eliminate redundant indicators with repeated information. The availability of the proposed method is illustrated via an example, and the key indicators in the enterprise diagnostic index system are found. Finally, the advantages of the proposed method are discussed using comparative analysis with existing methods. A rational and comprehensive enterprise diagnostic index system was constructed. The system can be used as a scientific basis for diagnosing the development of enterprises and providing an objective and effective reference. Full article

In recent decades, the hesitant fuzzy set theory has been used as a main tool to describe the hesitant fuzzy phenomenon, which usually exists in multiple attributes of decision making. However, in the general case concerning numerous decision-making problems, values of attributes are real numbers, and some decision makers are hesitant about these values. Consequently, the possibility of taking a number contains several possible values in the real number interval [0, 1]. As a result, the hesitant possibility of hesitant fuzzy events cannot be inferred from the given hesitant fuzzy set which only presents the hesitant membership degree with respect to an element belonging to this one. To address this problem, this paper explores the axiomatic system of the hesitant possibility measure from which the hesitant fuzzy theory is constructed. Firstly, a hesitant possibility measure from the pattern space to the power set of [0, 1] is defined, and some properties of this measure are discussed. Secondly, a hesitant fuzzy variable, which is a symmetric set-valued function on the hesitant possibility measure space, is proposed, and the distribution of this variable and one of its functions are studied. Finally, two examples are shown in order to explain the practical applications of the hesitant fuzzy variable in the hesitant fuzzy graph model and decision-making considering hesitant fuzzy attributes. The relevant research results of this paper provide an important mathematical tool for hesitant fuzzy information processing from another new angle different from the theory of hesitant fuzzy sets, and can be utilized to solve decision problems in light of the hesitant fuzzy value of multiple attributes. Full article

Multi-criteria decision-making (MCDM) plays a vibrant role in decision-making, and the characteristic object method (COMET) acts as a powerful tool for decision-making of complex problems. COMET technique allows using both symmetrical and asymmetrical triangular fuzzy numbers. The COMET technique is immune to the pivotal challenge of rank reversal paradox and is proficient at handling vagueness and hesitancy. Classical COMET is not designed for handling uncertainty data when the expert has a problem with the identification of the membership function. In this paper, symmetrical and asymmetrical normalized interval-valued triangular fuzzy numbers (NIVTFNs) are used for decision-making as the solution of the identified challenge. A new MCDM method based on the COMET method is developed by using the concept of NIVTFNs. A simple problem of MCDM in the form of an illustrative example is given to demonstrate the calculation procedure and accuracy of the proposed approach. Furthermore, we compare the solution of the proposed method, as interval preference, with the results obtained in the Technique for Order of Preference by Similarity to Ideal solution (TOPSIS) method (a certain preference number). Full article

Based on the continuous optimal aggregation operator, a novel distance measure is proposed to deal with interval intuitionistic fuzzy clustering problems. The optimal ordered weighted intuitionistic fuzzy quasi-averaging (OOWIFQ) operator and the continuous OOWIFQ operator are presented to aggregate all the values in an interval intuitionistic fuzzy number. Some of their desirable properties are also studied. The OOWIFQ operator can describe the fuzzy state of things more realistically and present the fuzzy properties more accurately. The opinions of experts are very important, the OOWIFQ operators take expert preferences into account to reduce systematic errors. Considering the hesitation of things and avoiding distortion of information, we put forward the distance measure for interval intuitionistic fuzzy numbers by using symmetric information entropy. Based on the continuous OOWIFQ operator and proposed distance measure, a new interval intuitionistic fuzzy clustering (IIFC) algorithm is proposed. The application in soil clustering shows the validity and practicability of the IIFC algorithm. Full article

Grouting-efficiency evaluation is a key element in grouting-construction control. However, most existing grouting-efficiency evaluation models do not consider the hesitation and bounded rationality of experts and have difficulty in handling the problem of incomplete decision-making information generated by experts. Furthermore, the diversity of the evaluation indicators used can be further improved. This study conducts a comprehensive evaluation model to address these problems. An objective and reasonable fuzzy evaluation method is demonstrated through the integration of interval-valued intuitionistic fuzzy sets, prospect theory, and improved D numbers. The secondary permeability index is introduced to establish a more scientific evaluation indicator system. The proposed model is implemented in evaluating the curtain-grouting efficiency of a hydropower station, and its consistency, representativeness, and superiority are validated and analyzed. Full article

The uncertainty and concurrence of randomness are considered when many practical problems are dealt with. To describe the aleatory uncertainty and imprecision in a neutrosophic environment and prevent the obliteration of more data, the concept of the probabilistic single-valued (interval) neutrosophic hesitant fuzzy set is introduced. By definition, we know that the probabilistic single-valued neutrosophic hesitant fuzzy set (PSVNHFS) is a special case of the probabilistic interval neutrosophic hesitant fuzzy set (PINHFS). PSVNHFSs can satisfy all the properties of PINHFSs. An example is given to illustrate that PINHFS compared to PSVNHFS is more general. Then, PINHFS is the main research object. The basic operational relations of PINHFS are studied, and the comparison method of probabilistic interval neutrosophic hesitant fuzzy numbers (PINHFNs) is proposed. Then, the probabilistic interval neutrosophic hesitant fuzzy weighted averaging (PINHFWA) and the probability interval neutrosophic hesitant fuzzy weighted geometric (PINHFWG) operators are presented. Some basic properties are investigated. Next, based on the PINHFWA and PINHFWG operators, a decision-making method under a probabilistic interval neutrosophic hesitant fuzzy circumstance is established. Finally, we apply this method to the issue of investment options. The validity and application of the new approach is demonstrated. Full article

The Bonferroni mean (BM) can be used in situations where the aggregated arguments are correlated. BM is very useful for solving decision-making problems. For describing fuzziness and vagueness more accurately, the interval-valued hesitant fuzzy set (IVHFS), which is a generalization of the hesitant fuzzy set (HFS), can be used to describe the membership degrees with interval numbers. The aim of this paper is to propose the interval-valued hesitant fuzzy Bonferroni mean (IVHFBM) for aggregating interval-valued hesitant fuzzy information. Furthermore, the weighted form of IVHFBM (IVHFWBM) is forwarded and, hereby, a multi-criteria group decision-making (MCGDM) method is established. A case study on the problem of evaluating research funding applications in China is analyzed. A comparison between the proposed method and existing ones demonstrates its practicability. Full article