چكيده به لاتين
Abstract:
The fuzzy linear fractional programming problem is an important planning tool in different areas such as engineering, business, finance, and economics. In this study, we propose the use of the (; r) acceptable optimal value for a linear fractional programming problem with fuzzy coefficients and fuzzy decision variables, as well as developing a method for com- puting them. To obtain acceptable (; r) optimal values, we take an α-cut on the objective function and r-cut on the constraints. We then formulate an equivalent bi-objective linear fractional programming problem to calculate the upper and lower bounds of the fully fuzzy LFP problem.
Using the upper and lower bounds obtained, we construct the mem- bership functions of the optimal values numerically. We illustrate the proposed procedure using numerical and real life examples.
Keywords: Bi-objective linear fractional programming problem، linear fractional programming problem، linear programming problem،Triangular fuzzy number
