A Multi-Criteria Decision-Making Approach based on TODIM and Choquet Integral within a Multiset Hesitant Fuzzy Environment

Hesitant fuzzy sets (HFSs), which were generalized from fuzzy sets, constrain the membership degree of an element to be a set of possible values between zero and one; furthermore if two or more decision-makers select the same value, it is only counted once. However, a situation where the evaluation value is repeated several times differs from one where the value appears only once. Multiset hesitant fuzzy sets (MHFSs) can deal effectively with a case where some values are repeated more than once in an HFS. In this paper, the new comparison method and corresponding distance of multiset hesitant fuzzy elements (MHFEs) are introduced. Then, based on the traditional TODIM and Choquet integral methods, a novel approach for multi-criteria group decision-making (MCGDM) problems, where the criteria are interdependent or interactive and the decision makers have a bounded rationality, is proposed for ranking alternatives. Finally, an example is provided in order to verify the developed approach and demonstrate its validity and feasibility. Furthermore, comparative analysis is presented by utilizing the same example as well.