Multicriteria optimization is critical in decision-making problems where conflicting objectives must be balanced simultaneously. Conventional optimization methods often fall short of capturing the uncertainty and imprecision inherent in real-world systems. Fuzzy logic provides an effective means to model such uncertainty. The Sugeno method is particularly attractive among the various fuzzy inference systems due to its ability to produce outputs directly via functional rule consequences. This paper presents a new mathematical overview and computational framework for multicriteria optimization based on the fuzzy Sugeno logic method. We consider a framework system with three decision variables and three criteria, where each criterion is represented by a fuzzy Sugeno inference system containing three rules. Detailed derivations of the fuzzy model, gradient computations, and the formation of a composite objective function are provided. Furthermore, we include a Python-based code that simulates the implementation of the framework, allowing the simultaneous optimization of conflicting objectives under uncertainty. Our approach facilitates robust decision-making in complex systems and can be extended to various practical applications.