A New Method for Fuzzy Multiobjective Linear Fractional Optimization Based on Median Functions of α-Cuts

Abstract

This paper proposes a novel method for fuzzy multiobjective linear fractional optimization based on median functions of α-cuts. The aim is to provide a robust framework that faithfully captures the inherent fuzziness of the data, thereby improving solution quality in uncertain environments. The methodology consists of four stages: defuzzification, linearization of the fractional objectives, aggregation, and resolution. A key theoretical result establishes the preservation of Pareto optimality between the original fuzzy problem and the transformed deterministic model. Numerical experiments, including a practical case study, show that the proposed method yields more stable and higher-performing solutions than existing approaches. The main contribution lies in the use of median functions, which provide a natural compromise between the lower and upper bounds of a fuzzy interval and offer a unified treatment for both triangular and trapezoidal fuzzy numbers.