University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 23 5 2026 10 01 A hybrid neuro-fuzzy-evolutionary framework for multi-objective robust optimization under granular uncertainty 9 36 10080 10.22111/ijfs.2026.53678.9501 EN Majid Darehmiraki Khatam Al-Anbia university of Behbahan Madineh Farnam Shahid Chamran University of Ahwaz Journal Article 2025 10 28 This paper introduces a Hybrid Neuro-Fuzzy-Evolutionary (HNFE) framework for multi-objective robust optimization under granular uncertainty. The framework achieves a novel synthesis of three computational paradigms: granular calculus for handling fuzzy uncertainty, evolutionary algorithms for global exploration, and recurrent neural networks for local refinement. Unlike existing methods that rely on a single paradigm, our tripartite architecture enables simultaneous handling of multiple uncertainty levels while maintaining both global exploration capabilities and local convergence properties.<br />The core theoretical contribution is the formulation of Granular Karush-Kuhn-Tucker (KKT) conditions, which provide a foundational optimality framework for fuzzy multi-objective optimization through α-cut decomposition and weighted aggregation. The HNFE framework operationalizes this through three components: a granular reformulation module that transforms fuzzy problems into crisp multi-objective formulations; an enhanced evolutionary engine with granular non-dominated sorting; and a neuro-dynamic refinement system based on recurrent neural networks that ensures local convergence to granularly optimal solutions.<br />Comprehensive theoretical analysis establishes the framework's global convergence to Pareto-optimal solutions under mild regularity conditions. The framework's robustness across varying uncertainty levels and problem complexities, coupled with its adaptive parameter control, makes it suitable for real-world applications in finance, manufacturing, and complex systems engineering. Extensive numerical experiments demonstrate superior performance in hypervolume, generational distance, and solution diversity compared to state-of-the-art methods, with statistical significance tests confirming these advantages.<br />This work represents a significant advance in fuzzy optimization by providing a unified framework that seamlessly integrates global exploration, local refinement, and rigorous uncertainty handling, establishing new standards for computational intelligence under uncertainty. https://ijfs.usb.ac.ir/article_10080_82c667eb051d70a86f1096be4ffb55a3.pdf