A Hesitant Fuzzy Linguistic Multi-criteria Decision-Making Approach Based on Regret Theory

Due to the uncertainty and hesitancy of decision makers in assessing alternatives, hesitant fuzzy linguistic term sets have been proposed recently to allow decision makers to provide several linguistic terms in the evaluation process and have been widely used to deal with multi-criteria decision-making problems. According to the regret theory, decision makers may care more about the regret values than the absolute values of alternatives under uncertainty. The hesitant linguistic fuzzy multi-criteria decision making based on regret theory is investigated in this paper. The regret value of each alternative to the other ones is defined, based on which, four types of best alternatives are defined taking into account the uncertainty and hesitancy. The relationship between different types of best alternatives is investigated to reflect different preferences of decision makers. Several models are established to derive the corresponding best alternatives. Comparing with the existing methods, the proposed method considers both the hesitancy and the regret behavior of decision makers and can identify different types of best alternatives. The proposed method can give a complete analysis about the hesitant fuzzy linguistic multi-criteria decision making and provide decision makers more choices. Examples are finally given to illustrate the proposed method.