In this paper, a linear programming problem with symmetric trapezoidal fuzzy number which is introduced by Ganesan et al. in [4] is generalized to a general kind of trapezoidal fuzzy number. In doing so, we first establish a new arithmetic operation for multiplication of two trapezoidal fuzzy numbers. in order to prepare a method for solving the fuzzy linear programming and the primal simplex algorithm, a general linear ranking function has been used 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 doesn’t essentially include 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.
