A parametric approach to fuzzy multi-objective linear fractional program: An alpha cut based method

In the multi-objective programming problem (MOPP), finding an efficient solution is challenging and partially encompasses some difficulties in practice. This paper presents an approach to address the multi-objective linear fractional programing problem with fuzzy coefficients (FMOLFPP). In the method, at first, the concept of alpha - cuts is used to change the fuzzy numbers into intervals. Therefore, the fuzzy problem is further changed into an interval-valued linear fractional programming problem (IVLFPP). Afterward, this problem is transformed into a linear programming problem (LPP) using a parametric approach and the weighted sum method. It is proven that the solution resulted from the LPP is at least a weakly epsilon - efficient solution. Two examples are given to illustrate the method.