Improving Solutions for a Fuzzy Random Multi-Objective Linear Fractional Program

Abstract

Mathematical techniques that combine fuzziness and stochastics are powerful tools for modelling and managing probabilistic, vague, and imprecise uncertainties. They are valuable because they can efficiently solve concrete problems in which data are affected by imprecision and randomness. From this perspective, this article proposes a new technique for converting multi-objective linear fractional programs whose coefficients are random and fuzzy. Using weights to represent decision-maker preferences, independent of $\alpha$-cuts representing satisfaction levels related to fuzzy quantities, transforms the random fuzzy program into an equivalent random fuzzy linear programming problem. Subsequently, the optimal solution of the random fuzzy linear programming problem is obtained within a class of optimal solutions of the weighted relative pseudo-random linear programming problem. The proposed method generates a multitude of solutions that correspond to the decision-maker's desired level of satisfaction. The solutions found in the didactic examples validate the theory. Finally, applying the method to a specific inventory management issue involving fuzzy and random trapezoidal parameters demonstrates its effectiveness and practical relevance.