Time-sequential hesitant fuzzy set and its application to multi-attribute decision making

The hesitant fuzzy set has been an important tool to address problems of decision making. There are several various improved hesitant fuzzy sets, such as dual hesitant fuzzy set, hesitant interval-valued fuzzy set, and intuitionistic hesitant fuzzy set, however, no one kind of improved fuzzy sets could reflect attitude characteristics of decision makers on time-sequences. In reality, time-sequence is one important sector to reflect hesitant situations as decision makers might have different knowledges of the same alternative at different moments. To perfect the description of such hesitant situations and obtain more reasonable results of decision making, we define a new kind of hesitant fuzzy set, namely, time-sequential hesitant fuzzy set. Meanwhile, its corresponding basic operators, score function and distance measures are proposed. We also propose the concept of fluctuated hesitant information to describe hesitant degrees of decision makers on time-sequences. By comprehensively utilizing the score function, fluctuated hesitant information and distance measures under time-sequential hesitant fuzzy set, a synthetic decision model is proposed. Two illustrated examples and one real-application are utilized to illustrate the effectiveness and advantage of the synthetic decision model under time-sequential hesitant fuzzy set.