Abstract: Hesitant fuzzy set is a useful tool to model the situation where people have hesitancy to provide their preferences over alternatives, and it has attracted more and more attention from researchers in recent years. However, few studies focus on the hesitant fuzzy stochastic multiple attribute decision making problems in which the regret aversion behavior of the decision makers is considered. In this paper, a stochastic decision method based on regret theory and group satisfaction degree is proposed to deal with the stochastic multiple attribute decision making problems, in which the attribute weights are completely unknown and the attribute values take the form of hesitant fuzzy elements. Firstly, a novel group satisfaction degree based on the variance and score of attribute value is defined to avoid the subjective randomness caused by the artificially given reference points in advance. Comparing with the existing method, the novel hesitant fuzzy group satisfaction degree can well reflect the group divergence and has the characteristic of higher distinguishability. Then, an optimization model based on the group satisfaction degree for attribute weights is constructed and the weight vector of the attributes can be obtained through solving the model. Secondly, on the basis of the regret theory, the regret and rejoice valued matrices are constructed by the pair-wise comparison of alternatives, and the ranking of alternatives can be obtained according to the total psychological perception value of the decision group. Lastly, a numerical example is given to demonstrate the applicability and feasibility of the proposed method. Also, a comparative analysis with other relevant methods is presented. By developing the stochastic multiple attribute decision method with hesitant fuzzy information, horizons of research are broadened, and thus the level of group decision making is raised under hesitant fuzzy environment.

Key words: hesitant fuzzy element, group satisfaction degree, regret theory, stochastic decision making