Optimizing Fully Fuzzy Linear Systems Using the Average Uniform Algorithm: A Fuzzy Data Modeling Approach

This paper presents an Enhanced Average Uniform Algorithm (E-AUA) for solving Fully Fuzzy Matrix Equations (FFME), addressing critical limitations in existing fuzzy optimization methods. Our approach combines sophisticated dual exploration-exploitation mechanisms with adaptive parameter management and fuzzy-specific operators to achieve superior performance in handling uncertain linear systems. Through comprehensive evaluation on systems ranging from 3×3 to 20×20 dimensions, E-AUA consistently outperforms established meta-heuristic algorithms including genetic algorithms, particle swarm optimization, simulated annealing, and differential evolution, achieving solution accuracies below 10-6with 100% success rates. The algorithm demonstrates exceptional scalability with rigorously provenO(TKn3) computational complexity and maintains robust convergence across diverse problem types including wellconditioned, ill-conditioned, and mixed-sign systems. Rigorous theoretical analysis establishes formal convergence guarantees under explicitly stated conditions, while ablation studies confirm the contribution of each algorithmic component. Practical validation through two real-world applications-supply chain optimization and energy system management-confirms applicability across domains, achieving 15% cost improvements over deterministic approaches and demonstrating superior performance on systems with up to 150 decision variables. Statistical validation through 50 independent runs with Wilcoxon signed-rank tests confirms significance atp< 0.001 levels, while comprehensive comparative analysis against recent optimization algorithms, including Honey Badger and Grey Wolf optimizers establishes E-AUA’s state-of-the-art performance.