An Intelligent Industry 5.0 Logistics Decision System: Circular Supply Chain Management With Fermatean Neutrosophic Hypersoft Sets And Machine Learning

Muhammad Tahir; Muhammad Imran Shahid

Authors

Muhammad Tahir Department of Mathematics, Institute of Numerical Sciences, Gomal University, Dera Ismail Khan, 29050, KPK, Pakistan Author https://orcid.org/0009-0003-6542-6264
Muhammad Imran Shahid Department of Mathematics and Statistics, University of Southern Punjab, Multan, Pakistan Author https://orcid.org/0000-0001-9563-1638

Keywords:

Fermatean Neutrosophic Hypersoft Sets, Circular Supply Chain, Industry 5.0, Machine Learning, Logistics Decision System, Deep Reinforcement Learning

Abstract

Industry 5.0 has transformed the logistics value chain with human-centricity, sustainability, and resilience at its core, with circular supply chain strategies playing a pivotal role through reuse, remanufacturing, and recycling. Circular logistics, however, brings complex uncertainties such as quality issues with returns, volume fluctuations, conflicting information, and multi-attribute decision-making, which cannot be captured by traditional models. The paper proposes a new model based on Fermatean Neutrosophic Hypersoft Sets (FNHSS) and machine learning to optimize circular supply chain management in the era of Industry 5.0. The framework makes four contributions: first, it provides a mathematical framework for FNHSS that accounts for three-dimensional uncertainty (truth, indeterminacy, and falsity) under Fermatean constraints (0 ≤ φ³ + υ³ ≤ 1), along with hypersoft multi-attribute parameterization; second, it introduces dual solution paths, including numerical defuzzification optimized using the Modified Distribution method and a deep reinforcement learning architecture based on a transformer encoder and a graph neural network (GNN); third, it proposes a circular economy reward function that balances logistics costs, returns, and circularity; fourth, it validates the framework through an automotive electric vehicle battery recycling case study. Empirical results show that the uncertainty capture index reaches 0.87, significantly above fuzzy machine learning baselines, with cost improvements of 6.16% and 1.99% compared to Type-1 fuzzy and intuitionistic fuzzy approaches, respectively. The numerical and ML solutions show no significant difference (p > 0.05), and the trained ML model enables constant-time inference essential for dynamic Industry 5.0 contexts. The FNHSS-ML architecture offers a robust approach for resilient, adaptable, and sustainable intelligent logistics systems.

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