An Innovative Approach to Solve Fuzzy Linear Fractional Programming Problems

Linear Fractional Programming is a mathematical optimization approach that addresses problems involving the optimization of a linear fractional objective function subject to linear constraints. We discussed approach to solving the fuzzy LFPP with and without equality constraints. We have solved this problem without converting it from fuzzy to crisp. First, we changed FLFPP into the FLPP. This problem was converted into parametric form then we solved it using the LU decomposition method to obtain the solution. We presented a numerical example with a real-life application for the simplicity of presenting the algorithm. While most researchers solve FLFPPs using the ranking function method, this method reduces the efficiency of the fuzzy problem. Linear fractional problems with inequality constraints sometimes do not have an optimal solution by using the LU decomposition method. Therefore, we conclude that there is a limitation for this LU decomposition method only for LFP problems with equality constraints.