Computational modelling under uncertainty: statistical mean approach to optimize fuzzy multi-objective linear programming problem with trapezoidal numbers

Abstract

This study presents a comprehensive approach to solving fuzzy multi-objective linear programming problems (FMOLPP) under uncertainty using trapezoidal fuzzy numbers. The authors propose a novel integration of Yager’s ranking method, the Big-M optimization technique, and Chandra Sen’s statistical mean methods to effectively convert fuzzy objectives into crisp values and optimize them. The methodology allows for managing multiple fuzzy objectives by ranking and aggregating them using various statistical means such as arithmetic, geometric, quadratic, harmonic, and Heronian averages. The model is implemented using TORA software and demonstrated through a detailed numerical example. The results validate the robustness and practicality of the proposed approach, showcasing consistent optimal solutions across all statistical methods. This research significantly enhances decision-making processes in uncertain environments by offering a structured, computationally efficient solution strategy for complex real-world optimization problems.