Probabilistic linguistic QUALIFLEX approach with possibility degree comparison

QUALIFLEX (QUALItative FLEXible multiple criteria method) is one of useful outranking methods for analyzing multiple criteria decision problems because of its flexibility with respect to the information of cardinal and ordinal. This paper developed a probabilistic linguistic QUALIFLEX method with possibility degree comparison method for dealing with group decision making problems, in which the evaluation information of alternatives are expressed by hesitant fuzzy linguistic sets and standard weights are partially known. Note that it is more reasonable using probabilistic linguistic term sets (PLTSs) to represent the whole viewpoint of group, which are got by combining HFLTSs. Firstly, the possibility degree formula for comparing PLTSs is proposed and their properties are discussed. Then, the concordance/ discordance index, the weighted concordance/ discordance index, and the comprehensive concordance/discordance index are defined by using the possibility degree comparison method. The optimal ordering order of the alternatives is obtained based on the study of all possible permutations of alternatives and the establishment of linear programming models. Finally, an application study and a comparative analysis with two cases are conducted to indicate the feasibility, reasonability and applicability of the proposed methodology.