Some approaches to solving fuzzy linear fractional programming

An important planning tool is linear fuzzy fractional programming, it is used in various fields such as business, engineering, and others. We are trying to get one of the direct and effective methods that contain some arithmetic operations to obtain the optimal real values through which a multi-objective fuzzy linear programming problem (MOFLFPP) is transformed into a linear programming problem (LPP) through the use of α-cut and MaxMin technique. The field of application is Iraqi Light Industries Company and chose the best products that must be protected which achieved a possible greatest profit ratio to less cost, Where the paper will include two sections, the first is concerned with describing the data and building the mathematical model for the problem (MOFLFPP) related to the research problem. The second section deals with trying to solve the model as well as finding the optimal solution, which represents determining the best and optimal production mix that achieves maximum profits at the lowest costs in light of the restrictions imposed on the production process, which may limit the company’s ability to provide products in the required quantity and the right time. The proposed methodology proved effective in solving multi-objective linear fractional programming problems with fuzzy coefficients (MOLFPP). While the previous approach produced results between (0.19904, 0.3406), our technique improved them to (0.2087, 0.3431), demonstrating higher reliability and efficiency with an ε-optimal unique solution.