Efficient Fuzzy Solutions for Linear Fractional Programming Problems: Using Pentagonal Fuzzy Numbers and the Decomposition Method

This paper presents an efficient method for solving fully fuzzy linear fractional programming (FFLFP) problems using pentagonal fuzzy numbers (PFNs) and the decomposition method. In real-world decision-making, uncertainty is inevitable, and fuzzy set theory provides a powerful framework to model such uncertainty. The proposed approach decomposes the FFLFP problem into five independent linear fractional programming (LFP) problems. Each LFP is transformed into a linear programming (LP) problem using the Charnes and Cooper transformation and solved via the simplex method. The obtained solutions are then aggregated to construct an efficient fuzzy solution. A numerical example is provided to demonstrate the effectiveness and applicability of the method. The results show that the proposed technique is accurate and suitable for solving complex optimization problems under uncertainty.