A ROBUST APPROACH FOR FUZZY MULTIOBJECTIVE LINEAR OPTIMIZATION VIA BANACH SPACE EMBEDDING AND OPTIMAL TRANSFORMATION TECHNIQUE

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Résumé

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 func-
tions 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 de-
terministic 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 op-
timality. The numerical results show an improvement in robustness and performance, with balanced and realistic
solutions.

Mots-clés

fuzzy optimization; multiobjective optimization; embedding theorem; optimal transformation; Pareto optimality.