A Novel Generalized Hybrid Aggregation Operators Based on Picture Hesitant Fuzzy Sets and Their Application in Decision Making

Abstract

Picture hesitant fuzzy (PHF) set (PHFS) is a mixture of picture fuzzy set (PFS) and hesitant fuzzy set (HFS) to cope with all existing drawbacks. The PHFS contains the positive, the abstinence and the negative grades in the form of finite subset of [0,1]. The drawback of the PHFS is that the sum of maximum of positive, maximum of abstinence and maximum of negative grades is belonging to [0,1]. Keeping the advantages of the PHFS, in this paper the notion of PHF generalized weighted averaging (PHFGWA) operator, PHF generalized ordered weighted averaging (PHFGOWA) operator, PHF generalized hybrid weighted averaging (PHFGHWA) operator is initiated. The properties of the established work and their related results are also identified. Further, these established operators are utilized in the environment of decision making. Finally, the established work is compared with some existing works with the help of examples to express the reliability and feasibility of the explored measures.