Solving a Fuzzy Linear Programming Problem with Triangular Membership Function

Se Ho Oh; Myungho Lee  and Wooyoung Song

doi:10.17485/ijst/2015/v8iS9/68287

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Solving a Fuzzy Linear Programming Problem with Triangular Membership Function

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2015/v8iS9/68287

Year: 2015, Volume: 8, Issue: Supplementary 9, Pages: 1-5

Original Article

Solving a Fuzzy Linear Programming Problem with Triangular Membership Function

Se-Ho Oh^1* , Myungho Lee² and Wooyoung Song²

¹Department of Industrial Engineering, Cheongju University, Korea; [email protected]
²Department of Electronic Engineering, Cheongju University; Korea

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

This paper deals with the linear problem under the equality constraints whose right hand side parameters are asymmetric triangular fuzzy numbers. The right hand side values are defuzzified by using the triangular membership functions. Each of these triangular functions is algebraically replaced with two piecewise linear functions. And the desired objective value is also a fuzzy number. The membership function of the objective is assumed to be piecewise linear. Then, according to Zimmermann’s approach, by using these membership functions and the max-min rule, the fuzzy linear problem is transformed into the crisp linear programming problem. Consequently a fuzzy solution is obtained by solving this linear programming problem.
Keywords: Fuzzy Linear Programming, Max-Min Rule, Piecewise Linear, Triangular Membership Function