A Generalized Model for Fuzzy Linear Programs with Trapezoidal Fuzzy Numbers

Abstract

‎ In this paper, we generalize a linear programming problem with symmetric trapezoidal ‎fuzzy number which is introduced by Ganesan and et al. in [3] to a general kind of trapezoidal fuzzy number. In this way, we first establish a new ‏arithmetic operation for multiplication of two ‏trapezoidal fuzzy numbers. Then in order to ‎preparing a method for solving the fuzzy linear programming as well as the primal simplex ‎algorithm, we use a general linear ranking function as a convenient approach in the literature. In fact, our main contribution in this work is based on 3 items: 1) Extending the current fuzzy linear program to a general kind which is not essentially including the symmetric trapezoidal fuzzy number‎s ‎‏,‏ 2) Defining a new multiplication role of two trapezoidal fuzzy number‎s‎, 3) Establishing a fuzzy primal simplex algorithm for solving the generalized model. We in particular emphasize that this study can be used for establishing fuzzy dual simplex algorithm, fuzzy primal-dual simplex algorithm, fuzzy multi objective linear programming and the other similar methods which are appeared in the literature.