Linear fractional programming problems subject to mixed fuzzy relation equations

In this paper, the problem of linear fractional programming problem provided to Mixed Fuzzy Relation Equation (MFRE) is studied. The structure of its feasible domain is firstly investigated. It is shown that the complete solution set is determined by a maximum solution and a finite number of minimal solutions. With regard to the structure, the problem is converted to some traditional fractional programming problems, then Charnes and Copper’s transformation is applied to convert them to linear programming problems. Finally, we can easily find the optimal solution of the original problem by solving the linear programming problems. A numerical example is given to illustrate the process.