Solving Fuzzy Linear Programming Problems with Linear Membership Function

This paper proposes the ``modified subgradient method'' and uses it for solving fuzzy programming problems in which both the right-hand side and the technological coefficients are fuzzy numbers and compares it with well known ``fuzzy decisive set method''.

Abstract

In this paper, we concentrate on two kinds of fuzzy linear programming problems: linear programming problems with only fuzzy technological coefficients and linear programming problems in which both the right-hand side and the technological coefficients are fuzzy numbers. We consider here only the case of fuzzy numbers with linear membership functions. The symmetric method of Bellman and Zadeh [2] is used for a defuzzification of these problems. The crisp problems obtained after the defuzzification are non-linear and even non-convex in general. We propose here the ``modified subgradient method'' and use it for solving these problems. We also compare the new proposed method with well known ``fuzzy decisive set method''. Finally, we give illustrative examples and their numerical solutions.