Fuzzy multiple criteria decision-making via an inverse function-based total utility approach

Abstract

This work presents ranking alternatives under fuzzy multiple criteria decision making (MCDM) via an inverse function-based total utility approach, where ratings of alternatives versus qualitative criteria as well as importance weights of all criteria are assessed in linguistic values represented by fuzzy numbers. Membership functions of the final fuzzy values of alternatives can be developed; some of their properties are investigated and proved. The right utility is obtained from the inverse function of right membership function of the final fuzzy value and the inverse function of maximizing set, while the left utility is obtained from the inverse function of left membership function of the final fuzzy value and the inverse function of minimizing set. Total utility is the sum of the right and left utilities. A larger total utility indicates that the corresponding alternative is more favorable. The ranking of fuzzy numbers can be clearly formulated to increase the applicability of the suggested fuzzy MCDM model. A numerical example demonstrates the feasibility of the proposed method, and some comparisons are provided to reveal robustness and advantages of the proposed method.