A likelihood-based QUALIFLEX method with interval type-2 fuzzy sets for multiple criteria decision analysis

The aim of this paper is to develop a likelihood-based QUALIFLEX method with interval type-2 fuzzy sets for multiple criteria decision analysis. This paper considers the context of interval type-2 trapezoidal fuzzy numbers and also introduces an extended concept of likelihoods of interval type-2 fuzzy preference relations. The concepts of lower and upper likelihoods are presented to serve as lower and upper bounds, respectively, of the possibility of preference relations and then to determine the likelihoods between interval type-2 trapezoidal fuzzy numbers. This paper uses a likelihood-based comparison between evaluative ratings to propose the concepts of concordance indices and comprehensive concordance indices for evaluating the permutations of alternatives corresponding to criterion-by-criterion consistency. By employing the signed distance-based method or the optimal membership-degree-determination method, the best permutation and its corresponding optimal ranking order of the alternatives can be acquired through a comparison of all of the comprehensive concordance indices. The applicability and effectiveness of the proposed method are illustrated with a medical decision-making problem that addresses the selection of treatment options. Additionally, a comparative analysis is performed with some relevant multiple criteria decision-making methods to demonstrate the advantages of the likelihood-based QUALIFLEX method. Finally, an analysis through computational experiments is conducted to examine the implementation efficiency of the proposed method.