A nonlinear programming approach to solve MADM problem with triangular fuzzy preference and non-preference information

In this paper, we present a new approach to solve multi-attribute decision making (MADM) problems considering subjective preferences and non-preferences of the decision maker in the form of triangular fuzzy preference relations and triangular fuzzy non-preference relations, respectively. Some important characteristics of these relations are used to form non-linear programming problems corresponding to lower, middle, and upper limits of the triangular fuzzy numbers. The optimization problems corresponding to lower and upper limits are solved to obtain corresponding limits of basic triangular fuzzy multiplicative preference weights (TFMPWs) and basic triangular fuzzy multiplicative non-preference weights (TFMNPWs). The obtained optimal weight values are used to find the modal values of TFMPWs and TFMNPWs that helps in the ranking of the alternatives. The working of the proposed approach is demonstrated by solving a MADM problem from the literature. Furthermore, to validate the superiority of the proposed approach, a comparative analysis with similar existing approaches has been provided. The obtained results reveal the applicability and usefulness of the proposed approach.