A hybrid neuro-fuzzy-evolutionary framework for multi-objective robust optimization under granular uncertainty

Document Type : Research Paper

Authors

1 Khatam Al-Anbia university of Behbahan

2 Shahid Chamran University of Ahwaz

10.22111/ijfs.2026.53678.9501

Abstract

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.
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.
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.
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.

Keywords

Main Subjects

References

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Iranian Journal of Fuzzy Systems
Volume 23, Issue 5
September and October 2026
Pages 9-36

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