Document Type : Research Paper
1 Department of Operations Research, Faculty of Mathematical Sciences, University of Mazandaran
2 Department of Mathematics, University of Mazandaran, Babolsar, Iran
3 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.