The TODIM analysis approach based on novel measured functions under hesitant fuzzy environment

Hesitant fuzzy set (HFS) is used to deal with the situations in which the decision makers hesitate among several values to assess an indicator, alternative, variable, etc. Recently, the multi-criteria decision making (MCDM) problems with hesitant fuzzy information have received increasing attentions and many corresponding MCDM methods have also been developed, but none of them can be used to solve the MCDM problems in case of considering the decision maker’s psychological behavior. In this study, we extend the TODIM (an acronym in Portuguese of interactive and multi-criteria decision making) method, which is based on prospect theory and can effectively capture the decision maker’s psychological behavior, to solve this type of problems under hesitant fuzzy environment. Firstly, we develop two novel measured functions for comparing the magnitude of hesitant fuzzy elements and interval-valued hesitant fuzzy elements, which are more reasonable and effective compared with the existing measured functions. Then, we calculate the dominance degree of each alternative related to the others based on novel measured functions and distance measures. By aggregating these dominance degrees, we can further obtain the overall value of each alternative and whereby rank the alternatives. Finally, a decision making problem that concerns the evaluation and ranking of the service quality among domestic airlines is used to illustrate the validity and applicability of the proposed method.