Fermatean Neutrosophic Hypersoft Set and Its Application to Impact Analysis of Green Power Trading in Uncertain Electricity Markets

The transition toward low-carbon economies has accelerated the adoption of Green Power Trading mechanisms, where renewable energy resources are traded across distributed markets. These markets are inherently uncertain because of changeable generation, dynamic pricing, regulatory variability, and various sustainability goals. To address this challenge, we propose a novel decision-making framework based on the Fermatean Neutrosophic HyperSoft Set (FNHSS), an innovative extension of HyperSoft Sets that integrates the expressive power of Fermatean Neutrosophic logic. FNHSS is introduced to allow representation and processing of multi-dimensional attribute tuples while capturing higher-order uncertainty through independent memberships under Fermatean constraints. Our study formalizes the definition of FNHSS, then establishes its set-theoretic and algebraic operations, providing illustrative examples from uncertain electricity market scenarios. Then, we contribute new distance measures that are inspired by Chebyshev-based distance computation to account for all attribute tuples in FNHSS for robust similarity assessment. We design a new scoring methodology that aggregates evaluations across all parameter–subparameter tuples, incorporating amplification and attenuation factors for Neutrosophic components. This score can be later used in a complete decision-making pipeline to rank alternatives according to global score, to ensure scalability and interpretability. A comprehensive case study on selecting the most sustainable warehouse location for an international e-commerce company in the Middle East and North Africa (MENA) region is conducted. Results demonstrate that the proposed FNHSS-based ranking procedure effectively integrates multiple conflicting parameters, while managing uncertainty and attribute interdependence. FNHSS not only opens new avenues for advanced decision-making under uncertainty, but also paves the way for advanced applications in supply chain management, energy systems, environmental planning, and strategic resource allocation.