Towards a New Approach in Complex Neutrosophic Soft Ring Theory

This paper focuses on investigating the algebraic structures within the complex neutrosophic soft model. Two key concepts, the complex neutrosophic soft ring (CNSR) and the complex neutrosophic soft ideal (CNSI), are introduced. The former integrates the characteristics of complex neutrosophic soft sets with the foundational principles of ring theory, to effectively address the issue of uncertainty and indeterminacy in a ring environment using complex neutrosophic membership values. The latter, on the other hand, are specific subsets of CNSRs with unique properties that play important roles in the study of ring theory. We examine and validate the algebraic properties of both CNSRs and CNSIs, enhancing the understanding of their algebraic behaviors and interactions. Specifically, we explore the connection between CNSRs and soft rings, offering insights into how CNSRs align with the broader framework of soft rings while emphazising the distinctive features of complex neutrosophic soft structures in algebraic analyses. Furthermore, we determine the relationships between CNSRs and neutrosophic soft rings, as well as between CNSIs and neutrosophic soft ideals. This thorough analysis aims to advance the knowledge of CNSRs and CNSIs, contributing to algebraic analysis and its application in managing uncertainty and vagueness.