Solving fuzzy linear programming problems with piecewise linear membership functions by the determination of a crisp maximizing decision

In this paper, we concentrate on 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 function. The determination of a crisp maximizing decision [2] is used for a defuzzification of these problems. The crisp problems obtained after the defuzzification are non-linear and non-convex in general. We propose here the ”augmented lagrangian penalty function 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 example and this solve by the new proposed method and compare the numerical solution with the solution obtained from fuzzy decisive set method.

Keywords:

Fuzzy linear programming , fuzzy number , augmented lagrangian penalty function method , fuzzy decisive set method