Neutrosophication as a General Framework for Regret Theory, Grey System Theory, and Three-Way Decision Models

Abstract

 Neutrosophy represents a comprehensive philosophical and mathematical framework for 
the study of neutrality, indeterminacy, and the interaction between opposites. The subsequent 
development of Refined Neutrosophy and Refined Neutrosophication significantly expanded the 
applicability of neutrosophic concepts to decision sciences, artificial intelligence, engineering, 
economics, and uncertainty modeling. This paper demonstrates that several influential theories 
developed independently in decision sciences and systems analysis—namely Regret Theory, Grey 
System Theory, and Three-Way Decision Theory—can be interpreted as particular cases of 
Neutrosophication. A formal Neutrosophication Operator is introduced to show how binary 
frameworks are transformed into triadic neutrosophic structures. We further demonstrate that 
Three-Way Decision models arise naturally from Neutrosophic Probability and that n-Way Decision 
models emerge as particular cases of Refined Neutrosophy. The proposed framework establishes 
Neutrosophy as a unifying meta-theory capable of integrating multiple approaches to uncertainty, 
partial knowledge, and decision-making under indeterminate conditions. 

DOI 10.5281/zenodo.20609950