CHFS: Complex hesitant fuzzy sets‐their applications to decision making with different and innovative distance measures

Abstract

The objective of the authors is to establish an innovative concept of the complex hesitant fuzzy set (CHFS), which is the combination of the hesitant fuzzy set and the complex fuzzy set to manage complex and awkward information in the real-decision theory. The structure and the basic properties of the proposed set are studied in detail. Based on the internal structure of the set and to find the degree of the discrimination between the pairs of the CHFSs, the generalized distance measures and modified generalized distance measures are defined. Several properties and their relationship between them are derived in detail. Also, several cases of the proposed measures are exposed which reduce them to the existing studies. Furthermore, based on these proposed measures, a decision-making approach is established under the uncertain environment and several numerical examples are given to examine the feasibility and validity of the explored measures. Finally, the credibility of the modified and parameterized distance measures based on CHFSs is verified by comparing them with some existing measures. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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

“…where λ > 0. If we put λ = 1 and λ = 2, then we get complex hesitant normalized hamming distance [41], and complex hesitant normalized Euclidean distance [41] respectively as follows:…”

“…From Table 1, we see that the ranking order by utilizing the proposed distance measures are the same as compared with the existing distances. However the distance measures proposed in [12] and [41] are the special cases of the distances developed in this paper. Therefore, the proposed distance measures are the generalization of the existing distance measures.…”

“…Rani and Garg [40] defined the distance and similarity measures for CIFSs. Garg et al [41] also introduced the distance and similarity measures for CHFSs.…”

Picture Fuzzy N-Soft Sets and Their Applications in Decision-Making Problems

“…In near future, we aim to discuss this study in the environment of spherical fuzzy sets, T-spherical fuzzy sets [47], the environment of bipolar soft sets [48], etc. [49][50][51][52].…”

Neutrality aggregation operators based on complex q‐rung orthopair fuzzy sets and their applications in multiattribute decision‐making problems

“…The theory of CFS has received extensive attention from distinguished scholars and has been reported in numerous studies. [32][33][34][35] Since CFS does not educate anything regarding the disagrees of the object and hence the methods based on them are limited in nature. Subsequently, CFS was improved into the complex IFS (CIFS) theory by Alkouri and Salleh.…”