tailieunhanh - Penalty method for fuzzy linear programming with trapezoidal numbers

In this paper we shall propose an algorithm for solving fuzzy linear programming problems with trapezoidal numbers using a penalty method. We will transform the problem of maximizing a function having trapezoidal fuzzy number values under some constraints into a deterministic multi-objective programming problem by penalizing the objective function for possible constraint violation. | Yugoslav Journal of Operations Research Vol 19 (2009), Number 1, 149-156 DOI: PENALTY METHOD FOR FUZZY LINEAR PROGRAMMING WITH TRAPEZOIDAL NUMBERS Bogdana STANOJEVIĆ Transilvania University of Brasov, bpop@ Milan STANOJEVIĆ Faculty of Organizational Sciences, Belgrade milans@ Received: December 2007 / Accepted: June 2009 Abstract: In this paper we shall propose an algorithm for solving fuzzy linear programming problems with trapezoidal numbers using a penalty method. We will transform the problem of maximizing a function having trapezoidal fuzzy number values under some constraints into a deterministic multi-objective programming problem by penalizing the objective function for possible constraint violation. Furthermore, the obtained deterministic problem will have only unavoidable inequalities between trapezoidal fuzzy numbers parameters as constraints. Keywords: Linear programming, trapezoidal fuzzy number, penalty method. 1. INTRODUCTION Concepts of fuzzy sets theory have “crowded” into a lot of research fields since 1980, because of the great success of fuzzy logic application in the control systems theory. The real advantages of the fuzzy approach to solving optimization problems can be highlighted when its comparison to the stochastic methods is made in order to deal with imprecision [4, 6]. Starting with Zimmermann [8], a lot of papers have been written covering the field of fuzzy linear programming. Buckley and Feuring dealt with the fully fuzzified linear programming problem (FFLP) by establishing all the coefficients and variables of a linear program as fuzzy quantities [1]. They transformed the fully fuzzified programming problem into a multiobjective deterministic problem (MODP) which is, in the general case treated, non-linear. In such a case, the problem is transformed into a multi-objective fuzzy problem with М. Stanojević, B. Stanojević / Penality Method for Fuzzy 150 whose help the authors explore the .