Structural Insights into IUP-Algebras via Intuitionistic Neutrosophic Set Theory

This paper introduces and explores the concepts of intuitionistic neutrosophic IUP-subalgebras, IUP-ideals, IUP-filters, and strong IUP-ideals within the framework of IUP-algebras. By leveraging the principles of complement, characteristic, and level subsets, we present a detailed analysis of their structural properties and interrelationships. These innovative approaches not only enhance the theoretical foundations of intuitionistic neutrosophic set theory but also provide new insights into managing uncertainty in algebraic structures. The findings contribute significantly to the advancement of algebraic logic, offering novel perspectives for handling indeterminate, ambiguous, and incomplete information in mathematical systems. This study lays the groundwork for future research and potential applications of intuitionistic neutrosophic IUP-algebras in areas such as decision-making, computational intelligence, and information theory.