The Double Inverted Pendulum on a Cart presents a challenging platform for control system design due to its inherent nonlinearity and under-actuated nature. Traditional methods such as the Linear Quadratic Regulator requires linearization, limiting effectiveness. In contrast, Fuzzy Logic Control handle nonlinearity without precise feedback but pose design complexity, especially for systems with multiple inputs like the DIPC, presents significant challenges. This paper proposes a novel approach leveraging Genetic Algorithm optimization to streamline FLC design for the DIPC. By optimizing output membership functions, the GA-Fuzzy controller aims to reduce design time and human intervention, offering a more efficient and effective solution for controlling complex, nonlinear systems. Comparative analysis with LQR control will further assess the effectiveness and applicability of the proposed methodology.