Search Results (25)

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 Due to the introduction of hesitation in IF and PF sets, the approximate accuracy of classical rough sets is no longer applicable.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

Effective franchise selection is crucial for global brands like Pizza Hut to maintain consistent quality and operational excellence amidst a competitive landscape. This paper introduces a novel confidence-interval circular intuitionistic fuzzy set (CIC-IFS) framework, designed to address the intricate challenges of master and sub-franchise selection in the European market. By integrating competence coefficients of decision-makers into the final evaluations, the model allows for a more accurate representation of expert judgments. Decision-makers can choose from various scenarios, ranging from super pessimistic to super optimistic, using ten forms of aggregation operations over index matrices. The proposed approach leverages confidence intervals within the circular intuitionistic fuzzy set paradigm to capture the uncertainty, vagueness, and hesitancy inherent in the decision-making process. A case study involving Pizza Hut’s European operations demonstrates the model’s efficacy in differentiating potential franchisees and identifying those best aligned with the brand’s values. The results indicate a significant improvement in selection accuracy compared to traditional methods and other fuzzy approaches, thereby enabling Pizza Hut to make more informed decisions and solidify its market position. Full article

The evaluation of the shrinkage–swelling characteristic of expansive clay is of great significance, but it is a complex problem since the evaluation process involves numerous uncertain factors, such as randomness, non-subordination, and hesitation uncertainties. Here, an intuitionistic connection cloud model has been proposed to address this issue. First, an evaluation index system is established. According to the reliability of interval-valued evaluation indexes, the corresponding cloud numerical characteristic parameters are specified based on the membership interval generated by the intuitionistic fuzzy principle. Moreover, the improved conditional information entropy based on rough set theory is utilized to assign the index weight. Subsequently, combined with the weight, the intuitionistic connection degree of the sample to the classification standard is determined to identify the shrinkage–swelling grade. Finally, a case study on the shrinkage–swelling grade of untreated and lime-treated expansive clays in Hefei Xinqiao International Airport was performed to illustrate the validity and reliability of the model. The results show that the proposed model is reasonable and feasible for the evaluation of the shrinkage–swelling grade of untreated and lime-treated expansive clays. Full article

Initially, fuzzy sets and intuitionistic fuzzy sets were used to address real-world problems with imprecise data. Eventually, the notion of the hesitant fuzzy set was formulated to handle decision makers’ reluctance to accept asymmetric information. However, in certain scenarios, asymmetric information is gathered in terms of a possible range of acceptance and nonacceptance by players rather than specific values. Furthermore, decision makers exhibit some hesitancy regarding this information. In such a situation, all the aforementioned expansions of fuzzy sets are unable to accurately represent the scenario. The purpose of this article is to present asymmetric information situations in which the range of choices takes into account the hesitancy of players in accepting or not accepting information. To illustrate these problems, we develop matrix games that consider the payoffs of interval-valued intuitionistic hesitant fuzzy elements (IIHFEs). Dealing with these types of fuzzy programming problems requires a significant amount of effort. To solve these matrix games, we formulate two interval-valued intuitionistic hesitant fuzzy programming problems. Preserving the hesitant nature of the payoffs to determine the optimal strategies, these two problems are transformed into two nonlinear programming problems. This transformation involves using mathematical operations for IIHFEs. Here, we construct a novel aggregation operator of IIHFEs, viz., min-max operators of IIHFEs. This operator is suitable for applying the developed methodology. The cogency and applicability of the proposed methodology are verified through a numerical example based on the situation of conflict between hackers and defenders to prevent damage to cybersecurity. To validate the superiority of the proposed model along with the computed results, we provide comparisons with the existing models. Full article

It is difficult to describe the hesitation and uncertainty of experts by single-valued information, and the differences in the importance of attributes are often ignored during the decision-making process. This paper introduces the probability and interval values into Fermatean hesitant fuzzy set (FHFS) and creatively proposes the probabilistic interval-valued Fermatean hesitant fuzzy set (PIVFHFS) to deal with information loss. This new fuzzy set allows decision makers to use interval-valued information with probability to express their quantitative evaluation, which broadens the range of information expression, effectively reflects the important degree of different membership degrees, and can describe uncertain information more completely and accurately. Under the probabilistic interval-valued Fermatean hesitant fuzzy environment, several new aggregation operators based on Hamacher operation are proposed, including the probabilistic interval-valued Fermatean hesitant fuzzy Hamacher weighted averaging (PIVFHFHWA) operator and geometric (PIVFHFHWG) operator, and their basic properties and particular forms are studied. Then, considering the general correlation between different attributes, this paper defines the probabilistic interval-valued Fermatean hesitant fuzzy Hamacher Choquet integral averaging (PIVFHFHCIA) operator and geometric (PIVFHFHCIG) operator and discusses related properties. Finally, a multi-attribute decision-making (MADM) method is presented and applied to the decision-making problem of reducing carbon emissions of manufacturers in the supply chain. The stability and feasibility of this method are demonstrated by sensitivity analysis and comparative analysis. The proposed new operators can not only consider the correlation between various factors but also express the preference information of decision makers more effectively by using probability, thus avoiding information loss in decision-making progress to some extent. 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

Undergraduate teaching audit and evaluation (UTAE) plays a substantial role in the teaching quality assurance and monitoring of universities. It achieves the goal of selecting the best university for promoting the quality of higher education in China. Generally, the UTAE is a complex decision-making problem by considering competing evaluation criteria. Moreover, the evaluation information on the teaching quality of universities is often ambiguous and hesitant because of the vagueness existing in human judgments. Previous studies on UTAE have paid subtle attention towards the managing of linguistic expressions and the performance priority of universities. The interval-valued hesitant fuzzy linguistic sets (IVHFLSs) can effectively describe uncertainty, hesitancy, and inconsistency inherent in decision-making process. The ORESTE (organísation, rangement et Synthèse de données relarionnelles, in French) is a new outranking decision-making method which can show detailed distinctions between alternatives. Therefore, in this study, we propose a new UTAE approach based on the VHFLSs and ORESTE method to resolve the prioritization of universities for selecting the optimal university to benchmark. Specifically, the presented method handles the hesitant and uncertain linguistic expressions of experts by adopting the IVHFLSs and determines the ranking of universities with an extended ORESTE approach. Finally, a practical UTAE example illustrates the feasibility the proposed approach and a comparison analysis provides grounding for the superiority of the integrated approach. When the obtained results are evaluated, U₂ has been determined as the best university. The results indicate the good performance of the proposed UTAE approach in evaluating and improving the teaching quality of universities. Full article

Source code clone detection, which can identify code fragments with similar functions, plays a significant role in software development and quality assurance. Existing methods either extract single syntactic or semantic information, or ignore the associated information between code statements in different structures. It is difficult for these methods to effectively detect clone pairs with similar functions. In this paper, we propose a new model based on a dual graph convolutional network (GCN) and interval-valued hesitant fuzzy set (IVHFS), which we named DG-IVHFS. Specifically, we simplified and grouped the abstract syntax tree (AST) of source code to obtain the group representations. The group representations of the AST, as well as the control flow graph (CFG) representations, were transformed into graph structures, and then we applied GCNs on them to learn dependencies between nodes. In addition, we introduced IVHFS into the model for a more comprehensive evaluation of similarity. Our experimental results demonstrated that the precision, recall, and F1-scores of DG-IVHFS on the BigCloneBench and GoogleCodeJam datasets reached 98, 97 and 97% and 98, 93 and 95%, respectively, exceeding current state-of-the-art models. Moreover, our model performed well in terms of time consumption. Full article

Blockchain technology is emerging and has high potential to improve and transform the agricultural supply chain. This study investigates the critical barriers to blockchain technology adoption in the Vietnamese agricultural supply chain using a novel interval-valued hesitant fuzzy Decision-Making Trial and Evaluation Laboratory (IVHF-DEMATEL) approach. The IVHF-DEMATEL technique is applied to identify cause-and-effect relationships and draw the influence-relations map of the barriers. In contrast to prior work, which converts fuzzy sets into crisp sets and then uses crisp set operations, this study is the first study to investigate the Vietnamese agricultural supply chain that uses fully hesitant fuzzy operations representing experts’ assessment without information loss during the conversion. Our results show that ‘lack of government regulation’, ‘lack of scalability and system speed’, ‘a large amount of resource and capital requirements’, and ‘lack of trust among agro-stakeholder or public perception’ are the main barriers. Consistent with previous studies, ‘lack of government regulation’ is the most significant barrier. The results also indicate the hesitant degree of each barrier and better inform decision-makers about uncertain situations. Moreover, a priority order for tackling barriers is proposed to accelerate blockchain adoption in the Vietnamese agricultural supply chain. Full article

This study aims to examine how the bilateral matching decision making of manufacturing enterprises that are seeking partners in the manufacturing supply chain can be improved by taking into consideration evaluation criteria for organizational quality-specific immunity. This study constructs an evaluation indicator system to measure organizational quality-specific immunity based on immune theory. The system’s evaluation criteria are based on the key components of organizational quality-specific immunity. We also construct bilateral matching evaluation and decision-making models using interval-valued hesitant fuzzy information and bidirectional projection technology (BMIHFIBPT). The interval-valued bilateral fuzzy bidirectional projection technology is applied to solve a combination satisfaction and matching optimization model. Empirical analysis is carried out to assess both the supply and demand sides of representative manufacturing enterprises in the manufacturing supply chain, match the main supply and demand bodies of two subjects, and help manufacturing enterprises select the optimal cooperation partners. The empirical analysis results indicate that the bilateral matching evaluation and decision-making models based on BMIHFIBPT can overcome the lack of information to some extent and help solve interval-valued hesitant fuzzy decision-making problems. In turn, the models can provide a basis for manufacturing enterprises to effectively select the best cooperation partners and conduct bilateral matching decision making in the manufacturing supply chain area that supports organizational quality-specific immunity. 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

Early warnings are an indispensable part of emergency management, which is a powerful way to eliminate or reduce the negative impacts caused by emergencies in advance. Early warning problems have been discussed from different perspectives and have obtained fruitful results. Information plays a critical role in all kinds of decision problems, with no exception for the early warning problem. There are various information types related to emergencies in real-world situations; however, existing early warning studies only considered a single information type, which might not describe the problem properly and comprehensively. To enrich existing early warning studies, a novel early warning method considering non-homogeneous information together with experts’ hesitation is proposed, in which numerical values, interval values, linguistic terms, and hesitant fuzzy linguistic terms are considered. To facilitate the computations with non-homogeneous information, a transformation process needs to be conducted. On such a basis, a fuzzy TOPSIS method based on alpha-level sets is employed to handle the transformed fuzzy information due to its superiority in obtaining information and its capacity to contain as much information as possible during the early warning process. Additionally, two different options are provided to analyze the status and tendency of early warning objects. Finally, an illustrative example about early warnings about landslides and a related comparison are conducted to demonstrate the novelty, superiority, and feasibility and validity of the proposed method. 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

A hesitant fuzzy set (HFS) and a cubic set (CS) are two independent approaches to deal with hesitancy and vagueness simultaneously. An HFS assigns an essential hesitant grade to each object in the universe, whereas a CS deals with uncertain information in terms of fuzzy sets as well as interval-valued fuzzy sets. A cubic hesitant fuzzy set (CHFS) is a new computational intelligence approach that combines CS and HFS. The primary objective of this paper is to define topological structure of CHFSs under P(R)-order as well as to develop a new topological data analysis technique. For these objectives, we propose the concept of “cubic hesitant fuzzy topology (CHF topology)”, which is based on CHFSs with both P(R)-order. The idea of CHF points gives rise to the study of several properties of CHF topology, such as CHF closure, CHF exterior, CHF interior, CHF frontier, etc. We also define the notion of CHF subspace and CHF base in CHF topology and related results. We proposed two algorithms for extended cubic hesitant fuzzy TOPSIS and CHF topology method, respectively. The symmetry of optimal decision is analyzed by computations with both algorithms. A numerical analysis is illustrated to discuss similar medical diagnoses. We also discuss a case study of heart failure diagnosis based on CHF information and the modified TOPSIS approach. Full article