Solving Fuzzy Linear Programming Problems with Linear Membership Functions.

Rafail N. Gasimov, K¨ur¸sat Yenilmez

Abstract

In this paper, we concentrate on two kinds of fuzzy linear programming problems: linear programming problems with only fuzzy technological coe?cients and linear programming problems in which both the right-hand side and the technological coe?cients 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 defuzzi?cation of these problems. The crisp problems obtained after the defuzzi?cation are non-linear and even non-convex in general.

We propose here the “modi?ed 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.

Key Words: Fuzzy linear programming; fuzzy number; modi?ed subgradient method; fuzzy decisive set method.

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