Document Type: Research Paper
Department of Operations Research, Faculty of Mathematical Sciences, University of Mazandaran
Department of Mathematics, University of Mazandaran, Babolsar, Iran
School of Mathematics and Information Science, Guangzhou University, Guangzhou, China.
In this paper, we generalize a linear programming problem with symmetric trapezoidal fuzzy number which is introduced by Ganesan and et al. in  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.