Complex hesitant fuzzy sets and its applications in multiple attributes decision-making problems

Abstract

Decision-makers (DMs) usually face many obstacles to give the right decision, multiplicity of them highlights a problem to represent a set of potential values to assign a collective membership degree of an object to a set for several DM’s opinions. However, a hesitant fuzzy set (HFS) deals with such problems. The complexity appears in DM’s opinion which can be changed for the same object but with different times/phases. Each of them has a set of potential values in different times/phases of an object. In this paper, the periodicity of hesitant fuzzy information is studied and applied by extending the range of HFS from [0, 1] to the unit disk in the complex plane to provide more ability for illustrating the full meaning of information to overcome the obstacles in decision making in the mathematical model. Moreover, the advantage of CHFS is that the amplitude and phase terms of CHFSs can represent hesitant fuzzy information, some basic operations on CHFS are also presented and we study its properties, in addition, several aggregation operators under CHFS are introduced, also, the relation between CHFS and complex intuitionistic fuzzy sets (CIFS) are presented. Finally, an efficient algorithm with a consistent process and an application in multiple attributes decision-making (MADM) problems are presented to show the effectiveness of the presented approach by using CHFS aggregation operators.

A novel MADM algorithm for physical education teaching quality evaluation based on 2-tuple linguistic neutrosophic numbers power heronian mean operators

“…Therefore, it is necessary to study the quality evaluation of physical education based on fuzzy multi-attribute decision-making [6][7][8][9][10][11]. Then, how to make the final judgment and ranking of the commodities in the commodity selection of the e-commerce platform, it is necessary to apply the fuzzy MADM method [12][13][14][15][16][17]. The fuzzy MADM method is mainly divided into two steps: one is to use the fuzzy MADM method to find out the fuzzy utility value of each scheme; the second is to use the fuzzy sorting method to deal with the fuzzy utility [18][19][20][21][22].…”

Priority Degrees and Distance Measures of Complex Hesitant Fuzzy Sets With Application to Multi-Criteria Decision Making

“…Therefore, to deal with such information, Ramot et al [23] introduced the concept of CFS as a generalization of FS and is characterized by complex valued membership degree. Talafha et al [24] extended the notion of CFS and introduced the concept of complex hesitant fuzzy set and a generalization of HFS with CFS. The CHFS [24] concept makes it one of the most effective strategies for dealing with unfavorable and complex data on practical decision-making problems.…”

“…Talafha et al [24] extended the notion of CFS and introduced the concept of complex hesitant fuzzy set and a generalization of HFS with CFS. The CHFS [24] concept makes it one of the most effective strategies for dealing with unfavorable and complex data on practical decision-making problems. CHFS [24], membership value has a complex value and is reflected in polar coordinates.…”

“…The CHFS [24] concept makes it one of the most effective strategies for dealing with unfavorable and complex data on practical decision-making problems. CHFS [24], membership value has a complex value and is reflected in polar coordinates. The amplitude term associated with the membership level gives the object size to the CHFS, and the phase time associated with the membership degrees provides additional details, which are often related to the passage of time.…”

“…CFS has gotten more attention among researchers in the last few years. Moreover, Talafha et al [24] extended the notion of CFS and introduced the concept of complex hesitant fuzzy (CHFS). CHFS is the combination of HFS and CFS.…”