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 complex hesitant fuzzy set (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.