A Novel Approach for Solving Multi-Objective Fuzzy-Stochastic Programming Problem by Using Goal Programming

Multi-objective optimization problems frequently arise in real-world systems where decision-makers face objectives that are conflicting, imprecise, or uncertain. Goal programming (GP) provides a systematic framework for resolving such conflicts by defining aspiration levels and minimizing deviations across multiple objectives. However, conventional models typically assume that all aspiration levels and parameters are precisely known, an assumption rarely satisfied in complex decision environments. Among various solution methods, approaches based on GP have been widely applied due to their flexibility in handling multi-objective decision problems under practical constraints. This study introduces a new methodology that transforms a fuzzy stochastic multi-objective programming problem into an equivalent GP model. The formulation incorporates fuzzy random variables (FRV) to represent both linguistic vagueness and probabilistic uncertainty in system parameters. The stochastic aspect is handled through an expectation-based transformation in the objective functions, while chance-constrained programming (CCP) is applied to maintain feasibility in the constraints. Triangular membership functions (TMF) are used to represent vague and ambiguous system information within the model, and following the transformation into a single-objective framework, Zimmermann's linear membership function is applied to evaluate the degree of goal satisfaction. Furthermore, a gradient-based conflict and non-conflict analysis is employed to assess interactions among objectives, which helps establish a structured assignment of aspiration levels and priorities. To validate the proposed approach, an existing numerical problem is considered, and its results are compared with those obtained from established methods.