Hesitant fuzzy information aggregation in decision making

Picture Hesitant Fuzzy Set and Its Application to Multiple Criteria Decision-Making

“…To deal with this situation, Torra [8] developed the HFS theory in which the membership degree is expressed by several possible values. Although a HFE can be given by any subset of [0, 1], in practice, HFS is commonly restricted to finite set in the MCDM problems [27]. Therefore, Bedregal at al.…”

“…To aggregate the hesitant fuzzy evaluation information, Xia and Xu [27] investigated the operations of HFEs, which is also valid for fusing UTHFEs.…”

“…In addition, several PF aggregation operators according to different operations were put forward [12,26]. Besides, a great time of hesitant fuzzy aggregation operators and their generalized forms were constructed [27], and several aggregation operators under dual hesitant fuzzy and dual interval-valued hesitant fuzzy environment were developed [28][29][30].…”

A note on operations of hesitant fuzzy sets

“…Copyright: the authorslems based on hesitant fuzzy sets, many hesitant fuzzy distance measures and aggregation operators have been proposed, such as the entropy of hesitant fuzzy sets and interval-valued hesitant fuzzy sets [6], generalized hesitant fuzzy synergetic weighted distance measure [14] and hesitant normalized Hamming, hesitant normalized Hausdorff distance and their generalizations [25]; interval-valued hesitant fuzzy aggregation operators [4], operations of generalized hesitant fuzzy sets according to score function and consistency function [15], hesitant fuzzy prioritized operators and hesitant interval-valued fuzzy aggregation operators [21,22], hesitant fuzzy ordered weighted averaging operator, hesitant fuzzy ordered weighted geometric operator and their generalization operators [24], TOPSIS and the maximizing deviation method with hesitant fuzzy information [26], the generalized hesitant fuzzy prioritized weighted average and generalized hesitant fuzzy prioritized weighted geometric operators [28], E-VIKOR method with hesitant fuzzy information for the multiple criteria decision making [31], hesitant fuzzy power aggregation operators [32], and hesitant fuzzy geometric Bonferroni means [33], etc. To deal with linguistic group decision making in hesitant situations, hesitant fuzzy linguistic term sets and corresponding with hesitant fuzzy linguistic aggregation have been proposed in [8-10, 16, 17, 23, 34].…”

Hesitant triangular intuitionistic fuzzy information and its application to multi-attribute decision making problem

“…In the research process of data information integration, the weighted averaging [4] operator, the ordered weighted averaging [20] operator, the weighted geometric [11] operator and the ordered weighted geometric [5,18] operator are four common data aggregating operators. As the theory of fuzzy sets have been proposed by Zadeh [21], Atanassov [1,2] gave the concept of intuitionistic fuzzy set, after the intuitionistic fuzzy weighted averaging, intuitionistic fuzzy ordered weighted averaging, intuitionistic fuzzy weighted geometric and intuitionistic fuzzy ordered weighted geometric operators were proposed, Torra [12,13] introduced the concept of hesitant fuzzy set which permitted membership to have a set of possible values in order that the hesitant fuzzy set can reflect the human's hesitant behavior, after which Xia and Xu [16] proposed some operations of hesitant fuzzy set. And Zhao et al [23] gave hesitant triangular fuzzy information and some aggregating operators like hesitant triangular fuzzy weighted averaging operator, hesitant triangular fuzzy ordered weighted averaging operator, hesitant triangular fuzzy weighted geometric operator, hesitant triangular fuzzy ordered weighted geometric operator to aggregate all the related information for MADM problems.…”