Frontiers in Artificial Intelligence Algorithm Optimization: Fermatean Fuzzy Deep Neural Networks for Uncertainty-Aware Decision-Making

With the rapid development of Artificial Intelligence (AI) technology, contemporary AI decision-making systems face significant challenges when dealing with high levels of uncertainty, imprecise data, and complex decision-making environments. Traditional deep learning models often struggle to maintain performance under such ambiguous conditions. Fermatean Fuzzy Theory (FFT), which utilizes advanced fuzzy numbers to comprehensively describe uncertainty, provides AI systems with enhanced flexibility and robustness. This is especially critical in fields such as multi-criteria decision-making, compromise programming, and reinforcement learning. To further improve the capability of uncertainty modeling, this paper proposes a novel Fermatean Fuzzy Deep Neural Network (FF-DNN) framework by systematically integrating Fermatean fuzzy theory into deep learning architectures. This innovative framework enables the rigorous fuzzification of input data, network weights, and activation functions, thereby significantly enhancing the overall robustness, generalization, and adaptability of neural networks operating in highly uncertain environments. From the perspective of artificial intelligence algorithm optimization, this study deeply explores the synergistic integration of fuzzy theory and deep learning for uncertainty-aware decision-making. Furthermore, this paper comprehensively examines the practical application of Fermatean Fuzzy Theory in AI decision-making, particularly highlighting its distinct advantages and inherent challenges in handling uncertainty and fuzziness. Finally, the study validates the effectiveness and superiority of the proposed FF-DNN framework through rigorous theoretical analysis and extensive case study discussions, demonstrating its potential to revolutionize complex decision support systems.