Entropy and Cross-entropy for Generalized Hesitant Fuzzy Information and Their Use in Multiple Attribute Decision Making

Abstract

In this paper, we present the entropy, cross‐entropy, and similarity measure for generalized hesitant fuzzy information and discuss their desirable properties. Some measure formulas are developed, and the relationships among them are investigated. We show that the similarity measure and entropy for generalized hesitant fuzzy information can be transformed by each other based on their axiomatic definitions. Then we develop two approaches for solving multiple attribute decision making, in which the attribute values are given in the form of generalized hesitant fuzzy elements (GHFEs). In the first approach, the attribute weight vector is determined by the generalized hesitant fuzzy entropies, and the optimal alternative is obtained by comparing the generalized hesitant fuzzy cross‐entropies between alternatives and positive‐ideal or negative‐ideal solutions; in the second approach, the attribute weight vector is derived from the maximizing deviation method and optimal alternative is obtained by using the technique for order preference by similarly to ideal solution (TOPSIS) method. Finally, an example is provided to illustrate the practicality and effectiveness of the developed approaches.

Some q-rung orthopair fuzzy maclaurin symmetric mean operators and their applications to potential evaluation of emerging technology commercialization

“…Finally, a numerical example is provided to illustrate the feasibility of the proposed methods and deliver the sensitivity analysis and comparative analysis. In a future study, we shall extend the MSM operator to decision making, risk analysis, and other fuzzy environments …”

“…In a future study, we shall extend the MSM operator to decision making, [67][68][69][70][71][72] risk analysis, and other fuzzy environments. [73][74][75][76][77][78][79][80][81][82][83][84][85][86]…”

An explainable multi-attribute decision model based on argumentation

“…Recently several researchers proposed fuzzy MADM models to handle criteria's evaluations with various complex fuzzinesses. As an example, to deal with degrees to which an alternative decision satisfies criteria, Park et al (2017) develop two approaches based on the concepts of entropy, cross-entropy, and similarity measure; Zhang (2016) propose one based on prioritised aggregation operator (more operators of this sort can be found in Luo et al (2003bLuo et al ( , 2015), and Yu et al (2016) also do so by developing several operators to aggregate all the criteria's evaluations. However, to the best of our knowledge, none of these approaches have any functionality for explaining the decisions they recommend.…”

Distribution-Based Approaches to Deriving Weights from Dual Hesitant Fuzzy Information

“…In the decision-making process, how to acquire the weight information of the attributes is recognized as a key issue. In general, these situations that most people encounter can be divided into two categories: (1) the weight information is completely unknown [16][17][18][19][20][21]. In this case, the weights are given relying on the criteria which are set in advance.…”