Fanyong Meng

Multi-attribute decision analysis under a linguistic hesitant fuzzy environment

In this paper, a new class of fuzzy sets called linguistic hesitant fuzzy sets (LHFSs) is defined, which can address the qualitative preferences of experts as well as reflect their hesitancy, uncertainty and inconsistency. Based on the defined operational laws of LHFSs and the order relationship, two linguistic hesitant fuzzy hybrid aggregation operators are defined: the generalized linguistic hesitant fuzzy hybrid weighted averaging (GLHFHWA) operator and the generalized linguistic hesitant fuzzy hybrid geometric mean (GLHFHGM) operator. Furthermore, to address the situation in which the elements in a set are interdependent, the generalized linguistic hesitant fuzzy hybrid Shapley weighted averaging (GLHFHSWA) operator and the generalized linguistic hesitant fuzzy hybrid Shapley geometric mean (GLHFHSGM) operator are presented, which are extensions of the GLHFHWA and GLHFHGM operators. Models designed to obtain the optimal fuzzy measures and additive measures on an attribute set and on an ordered set are, respectively, constructed. Then, an approach to linguistic hesitant fuzzy multi-attribute decision analysis is developed. Finally, two numerical examples are provided to demonstrate the practicality and efficiency of the proposed procedure.

A hesitant fuzzy linguistic multi-granularity decision making model based on distance measures

With respect to hesitant fuzzy linguistic term sets, a distance measure that can be seen as an extension of some linguistic distance measures is presented. Then, two generalized hesitant fuzzy linguistic weighted distance measures named the generalized hesitant fuzzy linguistic weighted distance GHFLWD measure and the generalized hesitant fuzzy linguistic 2-additive Shapley weighted distance GHFLASWD measure are defined, by which the comprehensive attribute values can be obtained. To consider the importance of the ordered positions and their internal interactions, the generalized hesitant fuzzy linguistic 2-additive Choquet Shapley weighted distance GHFLACSWD measure and the generalized hesitant fuzzy linguistic 2-additive Shapley Choquet weighted distance GHFLASCWD measure are presented. To cope with the situation where the weight information is incompletely known, models for the optimal weight vectors are constructed. Meanwhile, an approach to multi-granularity decision making with hesitant fuzzy linguistic preferences is proposed. Finally, an example is provided to illustrate the concrete application of the proposed method.

Linguistic Interval Hesitant Fuzzy Sets and Their Application in Decision Making

To cope with the hesitancy and uncertainty of the decision makers’ cognitions to decision-making problems, this paper introduces a new type of fuzzy sets called linguistic interval hesitant fuzzy sets. A linguistic interval hesitant fuzzy set is composed of several linguistic terms with each one having several interval membership degrees. Considering the application of linguistic interval hesitant fuzzy sets in decision making, an ordered relationship is offered, and several operational laws are defined. After that, several aggregation operators based on additive and fuzzy measures are introduced, by which the comprehensive attribute values can be obtained. Based on the defined distance measure, models for the optimal weight vectors are constructed. In addition, an approach to multi-attribute decision making with linguistic interval hesitant fuzzy information is developed. Finally, two numerical examples are provided to show the concrete application of the procedure.

Correlation Coefficients of Interval-Valued Hesitant Fuzzy Sets and Their Application Based on the Shapley Function

Interval‐valued hesitant fuzzy sets permit the membership degree of an element to have several possible interval values in [0, 1] rather than real numbers, which can well deal with inherent hesitancy and uncertainty in the human decision‐making process. In this paper, we first point out the issue of the existing correlation coefficients of interval‐valued hesitant fuzzy sets and then define several new ones, which do not have to consider the lengths of interval‐valued hesitant fuzzy elements and the arrangement of their possible interval values. Since the assumption that the elements in a set are independent is usually violated, we further define several Shapley weighted correlation coefficients, which consider their interactions. To deal with the situations where the elements are correlative and the weight formation is incompletely known, models for the optimal fuzzy measures on a feature set and on an attribute set are established, respectively. Finally, a procedure to pattern recognition and multiattribute decision making with incomplete weight information and interactive conditions is developed. Meanwhile, the corresponding examples are provided to show the practicality and feasibility of the proposed procedures.

Some uncertain generalized Shapley aggregation operators for multi-attribute group decision making

This paper studies some uncertain generalized aggregation operators based on the Shapley function, two of which are named the uncertain induced generalized Shapley averaging (UIGSA) operator and the uncertain induced generalized hybrid Shap- ley averaging (UIGHSA) operator. These two operators consider the interactive characteristics between elements and that of their ordered positions. Meanwhile, some important cases and desirable properties are studied. To simplify the complexity of solving a fuzzy measure, the uncertain induced generalized λ-Shapley averaging (UIGλSA) operator and the uncertain induced generalized hybrid λ-Shapley averaging (UIGHλSA) operator based on λ-fuzzy measures are presented. Finally, two new approaches to uncertain multi-attribute group decision making are developed, and a numerical example is provided to illustrate the proposed procedures.

An approach to interval-valued intuitionistic uncertain linguistic multi-attribute group decision making

The purpose of this paper is to investigate interval-valued intuitionistic uncertain linguistic multi-attribute group decision making with incomplete weight information and interactive conditions. In order to obtain the comprehensive attribute values of alternatives, the induced generalized Shapley interval-valued intuitionistic uncertain linguistic hybrid Choquet averaging (IGS-IVIULHCA) operator is defined, which globally considers not only the importance of elements and the ordered positions but also their correlations. Based on gray relational analysis (GRA) method, models for the optimal fuzzy measures are constructed. Then, a new decision approach is developed, which considers the interactive characteristics between elements in a set. Finally, a numerical example is presented to illustrate the proposed approach and demonstrate its practicality and effectiveness.

Uncertain linguistic hesitant fuzzy sets and their application in multi-attribute decision making

To denote the quantitative and qualitative fuzzy information simultaneously, this paper introduces a new type of fuzzy sets called uncertain linguistic hesitant fuzzy sets, which are denoted by an uncertain linguistic variable with several possible interval membership degrees. Considering the application of this type of fuzzy sets, several basic operational laws are defined, and several properties are studied. Meanwhile, an ordered relationship is introduced. Then, two types of uncertain linguistic hesitant fuzzy aggregation operators are defined. One uses additive measures, and the other is based on λ‐fuzzy measures. Then, a similarity measure is presented, by which models for the optimal weight vector are constructed. After that, an approach to uncertain linguistic hesitant fuzzy multi‐attribute decision making is developed. Finally, an illustrative example for evaluating corporate environmental performance is offered to show the concrete practicality of the procedure.

A value for games on augmenting systems with a coalition structure

The purpose of this paper is to discuss games on augmenting systems with a coalition structure, where all feasible subsets of the coalition structure and that of each union both form an augmenting system. A value named the augmenting symmetric Banzhaf coalitional value is introduced. The distribution of power in the Basque Parliament emerging is provided to illustrate the concrete application of the value. Meanwhile, two axiomatic systems are established.

Proportional coalition values for monotonic games on convex geometries with a coalition structure

Abstract A new model called games on convex geometries with a coalition structure is introduced, where all players and the coalition structure form a convex geometry, respectively. An explicit form of the proportional coalition solidarity value is given, which endows each union with the solidarity value in quotient games, and then allocates this value to players in a union following the proportions of their solidarity values in original games on convex geometries (i.e., without unions). Meanwhile, an axiomatization of this value is offered. Furthermore, the proportional coalition Shapley value is introduced. Its explicit form is offered, and an axiomatic system is studied.