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

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.