Fuzzy optimization is a branch of mathematical optimization that utilizes fuzzy set theory to tackle uncertainty, imprecision, and vagueness in decision-making processes. Unlike traditional optimization, which relies on precise data, fuzzy optimization accommodates the ambiguous data typical in complex real-world scenarios, such as in engineering and finance. Through fuzzy sets, decision variables and constraints are represented by degrees of membership instead of fixed values, allowing a broader range of feasible solutions. This approach supports linear and nonlinear programming, making it a versatile tool in fields where incomplete data and fluctuating conditions prevail. Consequently, fuzzy optimization has become essential for solving complex, real-world problems characterized by uncertainty, offering robust, adaptable methodologies for both theoretical and applied optimization. Separately, a fuzzy mathematical approach has been applied to analyze transgender issues in Tamil Nadu using a combined disjoint block fuzzy cognitive map. This method, based on the fuzzy cognitive map concept by Kandasamy and Smarandache [1], organizes and analyzes social problems by grouping concepts in large numbers. The study is structured into four sections: solutions to transgender issues, background on the combined disjoint block FCM, analysis of hidden patterns in transgender issues, and conclusions and recommendations based on the findings.