A Hybrid Neutrosophic Statistical–Game Theoretic Framework for Modeling Green Policy Dynamics of Coal Mining Enterprises Under Indeterminacy in Resource-Based Regions

Abstract

The industrial transformation of resource-based regions (RBRs) towards a 
sustainable and low-carbon economy remains a complex and uncertain endeavor. 
Traditional analytical tools often fall short in addressing the indeterminate, vague, and 
contradictory data that characterize environmental measurements and stakeholder 
behavior. To overcome these limitations, this paper proposes a novel hybrid framework 
that integrates Neutrosophic Statistics with Neutrosophic Game Theory to model 
environmental policy dynamics under uncertainty. We first introduce a new statistical 
measure, the Neutrosophic Variability Index (NVI), capable of capturing the spread of 
environmental data that contains imprecise, incomplete, or conflicting components. Using 
this enriched dataset, we then formulate a Neutrosophic Game Model involving three 
principal agents: government regulators, industrial firms, and civil society. Each agent's 
payoff function incorporates neutrosophic triplets’  truth (T), indeterminacy (I), and falsity 
(F)  to realistically reflect the multi-valued logic underlying policy decisions in complex 
ecological settings. Moreover, we define and prove the existence of a Neutrosophic Nash 
Equilibrium (NNE), which generalizes classical equilibrium by allowing players to 
operate under bounded indeterminacy. A real-world case study on green transformation 
in a coal-dependent region illustrates the utility and innovation of the model. Our results 
show that accounting for indeterminacy through neutrosophic measures significantly 
alters policy outcome predictions, enhances model realism, and provides policymakers 
with a robust decision-making tool that is mathematically rigorous and empirically 
grounded. 

DOI: 10.5281/zenodo.15540401