An approach based on $alpha$-cuts and max-min technique to linear fractional programming with fuzzy coefficients

This paper presents an efficient and straightforward method with less computational complexities to address the linear fractional programming with fuzzy coefficients (FLFPP). To construct the approach, the concept of $alpha$-cut is used to tackle the fuzzy numbers in addition to rank them.  Accordingly, the fuzzy problem is changed into a bi-objective linear fractional programming problem (BOLFPP) by the use of interval arithmetic. Afterwards, an equivalent BOLFPP is defined in terms of the membership functions of the objectives, which is transformed into a bi-objective linear programming problem (BOLPP) applying suitable non-linear variable transformations. Max-min theory is utilized to alter the BOLPP into a linear programming problem (LPP). It is proven that the optimal solution of the LPP is an $epsilon$-optimal solution for the fuzzy problem. Four numerical examples are given to illustrate the method and comparisons are made to show the efficiency.