Neutrosophic Γ-Near Rings and Their Application to Cryptocurrency Risk Evaluation Using Multi-Criteria Decision-Making Techniques

Abstract: This paper introduces and investigates a novel algebraic structure known as the neutrosophic Γ-near-ring, which integrates neutrosophic set theory with Γ-near-ring frameworks to address operations under uncertainty, indeterminacy, and contradiction. Each element in the proposedstructure is characterized by degrees of truth, indeterminacy, and falsity, thus enabling a more expressive and flexible modeling approach compared to traditional or fuzzy algebraic systems. Fundamental definitions are established, and key structural properties are explored. It is verified that the intersection of two neutrosophic Γ-near-rings results in a neutrosophic Γ-near-ring, ensuring stability. Moreover, we demonstrate that the union of two neutrosophic Γ-nearrings also a neutrosophic Γ-near-ring, provided one is contained within the other. Additionally, a oneone correspondence is recognized amidst of the neutrosophic and crisp forms of a Γ-near-ring, ensuring logical consistency and reversibility.The outcomes obtained here lay a theoretical foundation for further research and potential applications in various areas such as artificial intelligence, fuzzy logic, and algebraic modeling of uncertain systems.Key words: Neutrosophic Γ-near-ring, fuzzy Γ-near-ring.