Decision Making Using Modified S-Curve Membership Function in Fuzzy Linear Programming Problem

Abstract

In order to develop approaches to solve a fuzzy linear programming problem, it is necessary to study first the formulation of membership functions and then the methodology for applying the solution to real life problems. A S-curve membership function is proposed in this paper. It is important to note that S-curve membership function has to be flexible to describe the fuzziness in the problem. Fuzziness may occur in several levels of an industrial production management such as manpower requirements, resource availability such as software and the demand to be met. In order to show that the S-curve membership function works well for fuzzy problems, a numerical example is demonstrated. A thorough study on how the non linear membership function used in dealing with fuzzy parameters and fuzzy constraints is also presented. Only one case where all three coefficients (such as objective coefficients, technical coefficients and resource variables) that normally occur in production planning problem, are considered and fuzzified. However, there are several other cases. The result obtained from this paper is to provide confidence in using the proposed S-curve membership function in a real life production planning industrial problem.