A Robust Approach for Fuzzy Multiobjective Linear Optimization via Banach Space Embedding and Optimal Transformation Technique

Abstract

This paper proposes an innovative approach to solving fuzzy multiobjective linear optimization problems by combining the embedding theorem and an optimal transformation technique. The objective functions and fuzzy constraints are first embedded in a Banach space, where they are represented as parametric biobjective vectors. The application of a Riemann integral operator then allows them to be transformed into a deterministic and non-parametric form. Appropriate weights are introduced in order to limit compensatory effects and to ensure a non-empty admissible domain, leading to a weighted deterministic multiobjective problem of the same dimension. This problem is then aggregated into a single-objective nonlinear model, solvable by classical methods. The proposed transformations ensure the equivalence of the models and the preservation of Pareto optimality. The numerical results show an improvement in robustness and performance, with balanced and realistic solutions.