On Typical Hesitant Fuzzy Prioritized “or” Operator in Multi-Attribute Decision Making

Abstract

Since hesitant fuzzy set was proposed, multi-attribute decision making MADM with hesitant fuzzy information, which is also called hesitant fuzzy MADM, has been a hot research topic in decision theory. This paper investigates a special kind of hesitant fuzzy MADM problems in which the decision data are expressed by several possible values, and the evaluative attributes are in different priority levels. Firstly, we introduce the definitions of hesitant fuzzy t-norm and t-conorm by extending the notions of t-norm and t-conorm to the hesitant fuzzy environment and explore their constructions by means of t-norms and t-conorms. Then motivated by the prioritized or operator R. R. Yager, Prioritized aggregation operators, International Journal of Approximate Reasoning 2008;48:263-274, we develop the typical hesitant fuzzy prioritized or operator based on the developed hesitant fuzzy t-norms and t-conorms. In this operator, the degree of satisfaction of each alternative in each priority level is derived from a hesitant fuzzy t-conorm to preserve trade-offs among the attributes in the same priority level, and the priority weights of attributes are induced by a hesitant fuzzy t-norm to model the prioritization relationship among attributes. Furthermore, we apply the developed typical hesitant fuzzy prioritized or operator to solving the MADM problems in which the decision data are expressed by several possible values and the attributes are in different priority levels. In addition, two numerical examples are given to, respectively, illustrate the applicability and superiority of the developed aggregation operator by comparative analyses with previous research.