A Novel Method of Ranking Hesitant Fuzzy Values for Multiple Attribute Decision-Making Problems

Abstract

Despite of several generalizations of fuzzy set theory, the notion of hesitant fuzzy set (HFS), which permits the membership having a set of possible values, is interesting and very useful in modeling real‐life problems with anonymity. In this article, we introduce a new score function for ranking hesitant fuzzy elements (HFEs), which are the fundamental units of HFSs. Comparison with the existing score function shows that the proposed method meets all the well‐known properties of a ranking measure and has no counterintuitive examples. On the basis of the relationships between the aggregation operators for HFEs, we derive a series of interesting properties of the new score function. Finally, we apply the proposed score function to solve the hesitant fuzzy multiattribute decision‐making problems.

Note on lexicographical ordering

“…As assumed in many contributions made to the theory of HFEs (see e.g. [1,2,8,9] , Farhadinia [4] extended the HFE with fewer elements by repeating its maximum element until it has the same length with the other HFE.…”

“…We just list a few in the following: For examples, Wang et al [7] , Xia and Xu [8] , Xu and Xia [9] , Farhadinia [1,2,4] . In this technical note, we will focus on Farhadinia [4] to present an improvement.…”

Hesitant Fuzzy Worth: An innovative ranking methodology for hesitant fuzzy subsets

“…In the recent authoritative survey of HFSs [9], the authors summarize many useful and valuable decision making methods to solve hesitant fuzzy multicriteria decision making problems and propose further applications of HFSs to decision making. Within the extended field of Hesitancy in Fuzzy Sets, application papers that contribute to multicriteria decision making include [7], [10], [11], [12], [13], [14], [15] and [16]. Multiexpert multicriteria decision making under this requirement has been explored by Xia et al [17] or Tan et al [18] among others.…”

“…In our proposal the suitable application of scores on HFEs (specifically from [7], [10], and [19], who introduces a Geometric score, see also [23]) is complemented with a novel construction in this framework. It was imported from Social Choice -cf., the worth in Herrero [24]-to fuzzy soft set based decision making in [25].…”

Distance and Similarity Measures for Intuitionistic Hesitant Fuzzy Sets

“…A growing number of studies focus on the distance measure and the similarity measure for HFSs [14] and some extensions of HFS [15,16]. Distance measures are fundamentally important in various fields such as decision making [17][18], risk investment [19], and pattern recognition [20].…”