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

Abstract

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. 

DOI: 10.5281/zenodo.16707355