Construction of an appropriate membership function based on size of fuzzy set and mathematical programming

This paper proposes an extended approach to construct an appropriate membership function as objectively as possible. It is important to set an appropriate membership function to obtain a reasonable optimal solution for real-world decision making. The main academic contribution of our proposed approach is to integrate a general continuous and nonlinear function minimizing the subjectivity into an interval estimation by a heuristic method under a given probability density function based on real-world data. Our approach is an extend approach of Civanlar and Trussell's study. One of two main steps of our proposed approach is to set membership values which a decision maker confidently judges whether an element is included in the given set or not. Another is to obtain other values objectively by solving Civanlar and Trussell's mathematical programming problem with a nonlinear membership function. In this paper, the given membership function is approximately transformed into a piecewise linear membership function, and the appropriate values of parameters in the piecewise linear membership function are determined.