Multi-criteria decision-making with EDAS method and weighted operators for linguistic Fermatean hesitant fuzzy sets

: This paper is a further contribution to the problem of determining which fuzzy set operations are most appropriate for modeling a given situation. In review, a choice function, as defined by the author, is a mapping from the class of all fuzzy subsets of a given base space into the class of all random subsets of the same space such that any fuzzy set corresponds to some equivalent random set, where equivalence is with respect to membership function and one point coverage function, respectively. This, in turn, induces an equivalence class relation over the class of all random subsets of the given space. In previous work, a number of characterizations have been obtained for these fuzzy set and ordinary (and hence, random) set operations which have weak (i.e., up to the equivalence described above) homomorphic correspondence, relative to certain families of choice functions and joint distributions of random sets.

Revisiting fuzzy set operations: A rational approach for designing set operators for type-2 fuzzy sets and type-2 like fuzzy sets

The new arithmetic operations of non-normal fuzzy sets are studied in this paper by using the extension principle and considering the general aggregation function. Usually, the aggregation functions are taken to be the minimum function or t-norms. In this paper, we considered a general aggregation function to set up the arithmetic operations of non-normal fuzzy sets. In applications, the arithmetic operations of fuzzy sets are always transferred to the arithmetic operations of their corresponding α-level sets. When the aggregation function is taken to be the minimum function, this transformation is clearly realized. Since the general aggregation function was adopted in this paper, the concept of compatibility with α-level sets is needed and is proposed, which can cover the conventional case using minimum functions as the special case.

The hesitant fuzzy linguistic term set is a useful tool for decision makers to express their linguistic assessments over alternatives. In this paper, some new operations of hesitant fuzzy linguistic term sets are proposed based on 2-tuple linguistic aggregation operators and distribution linguistic aggregation operators, which can avoid the loss of information and make the aggregation results interpretable. Based on the proposed aggregation operators, an approach to multi-attribute group decision making with hesitant fuzzy linguistic term sets is developed. Finally, an example is used to demonstrate the feasibility and effectiveness of the proposed approach.

T-norms and t-conorms are basic operators of fuzzy logics. The classifications of these operators are significant problems. Some results of the classifications of fuzzy logics operators for fuzzy sets were given in [3,4]. In 2013, we defined the picture fuzzy sets [5,6] and in 2015 some representable t-norms operators and t-conorms operators were presented in [7,8]. In this paper, we will investigate the classification of representable picture t-norms and picture t-conorms operators for picture fuzzy sets.

Emerging trends in soft set theory and related topics.

An interpretation of membership functions and the properties of general probabilistic operators as fuzzy set operators — Part I: Case of type 1 fuzzy sets

An interpretation of membership functions and the properties of general probabilistic operators as fuzzy set operators. (II). Extension to three-valued and interval-valued fuzzy sets

Arithmetic operations of non-normal fuzzy sets using gradual numbers

Rough set theory can be generalized by induced topology through equivalence relations. Motivated by the work of generalization of the rough set via topology, the concept and properties of $ \tau-\mathfrak{K} $-fuzzy open (closed) sets are proposed. Considering the $ \tau-\mathfrak{K} $-fuzzy open (closed) sets, we have obtained the $ \tau-\mathfrak{K} $-fuzzy lower and upper approximations and also proved their properties. $ \tau-\mathfrak{K} $-fuzzy open sets can be represented as $ \tau-\mathfrak{K} $-open sets by $ \alpha $ level sets. The properties of $ \tau-\mathfrak{K} $-fuzzy approximations and fuzzy rough approximations on the basis of binary fuzzy relation are compared. Finally, an example and the decision method's algorithm to illustrate the $ \tau-\mathfrak{K} $-fuzzy approximation-based approach to decision making are presented.

Wireless sensor networks play an important role in economic production and social life. However, in recent years, the number of wireless sensor network vulnerabilities has been increasing rapidly, which makes wireless sensor networks face more and more severe challenges. It is of great significance to realize the quantitative evaluation of wireless sensor networks in order to maintain the service quality of wireless sensor networks more effectively. The evaluating problem of the service quality of wireless sensor networks is a kind of multiple attribute group decision-making (MAGDM) problem. In this paper, depending on the classical EDAS method, the EDAS method will be extended to interval-valued intuitionistic fuzzy sets (IVIFSs) to address some MAGDM issues. At first, some essential concepts of IVIFSs are briefly reviewed. Subsequently, relying on the CRITIC method, the attributes’ weights are decided. Furthermore, integrating the EDAS method with IVIFSs, IVIF-EDAS method is established, and all calculating procedures are depicted. Finally, an empirical application for evaluating the service quality of wireless sensor networks is given to demonstrate this novel algorithm, and some comparative analyses are made to confirm the merits of the designed method.

In recent decades, different extensional forms of fuzzy sets have been developed. However, these multitudinous fuzzy sets are unable to deal with quantitative information better. Motivated by fuzzy linguistic approach and hesitant fuzzy sets, the hesitant fuzzy linguistic term set was introduced and it is a more reasonable set to deal with quantitative information. During the process of multiple criteria decision making, it is necessary to propose some aggregation operators to handle hesitant fuzzy linguistic information. In this paper, two aggregation operators for hesitant fuzzy linguistic term sets are introduced, which are the hesitant fuzzy linguistic Bonferroni mean operator and the weighted hesitant fuzzy linguistic Bonferroni mean operator. Correspondingly, several properties of these two aggregation operators are discussed. Finally, a practical case is shown in order to express the application of these two aggregation operators. This case mainly discusses how to choose the best hospital about conducting the whole society resource management research included in a wisdom medical health system.

In this paper, we use a framework known as probabilistic linguistic computing (PLC) to achieve two goals. First, we demonstrate it as an easy-to-use laboratory for understanding existing fuzzy operators. This is achieved by projecting a fuzzy operator of interest into the PLC setting, arriving at a corresponding PLC operator, and hence revealing assumptions initially hidden in that operator. Second, we demonstrate PLC as a simple and general approach for the engineers to construct a wide range of fuzzy operators and measures that can be robustly used in their specialized applications. In particular, by explicating the assumptions hidden in the commonly used fuzzy set and fuzzy arithmetic operators, one is in position to develop other potentially more complex operators (such as fuzzy entropy measure or fuzzy partial correlation measures) that possess the same assumptions—these complex operators so developed can then be viewed as compatible and consistent with the commonly used fuzzy set and arithmetic operators.

The fuzzy set theory plays an important role in the modeling of the problems involving uncertain data. Some extensions of the fuzzy sets are needed due to the variety of problems encountered in real life. The concept of a hesitant fuzzy set is one of these extensions. Also, soft set theory, which is free from the difficulties of determining the membership function in fuzzy sets, plays an important role in dealing with uncertainty. In this study, we introduce the concept of hesitant fuzzy parameterized soft set as a generalization of the fuzzy parameterized soft sets. Then we define set-theoretical operations of the hesitant fuzzy parameterized soft sets and obtain some of their properties. We also improve a decision-making algorithm under the hesitant fuzzy parameterized soft environment and give an example to show the process of the algorithm. Finally, we compare the proposed decision-making algorithm with methods existing in the literature.

A nonzero fuzzy open set () of a fuzzy topological space is said to be fuzzy minimal open (resp. fuzzy maximal open) set if any fuzzy open set which is contained (resp. contains) in is either or itself (resp. either or itself). In this note, a new class of sets called fuzzy minimal open sets and fuzzy maximal open sets in fuzzy topological spaces are introduced and studied which are subclasses of open sets. Some basic properties and characterization theorems are also to be investigated.