Algorithms for regret theory and group satisfaction degree under interval-valued dual hesitant fuzzy sets in stochastic multiple attribute decision making method

Interval-value dual hesitant fuzzy set, first proposed by Ju et al. (Interval-valued dual hesitant fuzzy aggregation operators and their applications to multiple attribute decision making, 1203-1218, 2014). Multiple attribute decision making with dual hesitant fuzzy information is a new research topic since dual hesitant fuzzy set was firstly proposed, it has been widely studied in the fuzzy decision making literature. As a new generalization of fuzzy sets, interval-value dual hesitant fuzzy set (IVDHF) This article develops a multi-attribute decision making method considering the regret value theory and group satisfaction for the interval-value dual hesitant fuzzy element and incomplete weight information. Considering that decision makers have different level of the degree of evaluation, firstly, based on the score function and the accuracy function of the interval-valued hesitant fuzzy element, the deviation function of the interval-valued hesitant fuzzy set is defined. On this basis, a new group satisfaction is proposed. And then, for the situation where the information of attribute weight is incompletely known and completely unknown, some optimization models of attribute weight are established by using the new group satisfaction degree, and then the attribute weight can be determined. Finally, a real example of investment alternative evaluation is carried out to validate the implementation of the proposed approach.