Exploring the Structural Aspects of Interval-Valued Intuitionistic Neutrosophic Fuzzy Ẑ-Subalgebra

The article develops an updated methodology of interval-valued intuitionistic neutrosophic sets (IVINS) based on Ẑ-algebra theoretical structures. The new method presents an advanced solution to real-world uncertainties alongside inconsistent and indeterminate states found during decision-making and problem solving activities. The investigation follows up by proving fundamental principles for Ẑ-algebra under this neutrosophic extension. Researchers have deeply studied homomorphism properties and Cartesian product operations of interval-valued intuitionistic neutrosophic sets contained in Ẑ-algebras. Research applications of fuzzy set theory span multiple domains that include real-world, theoretical, and imaginary contexts. Multiple algebraic structures such as BCK/BCI-algebras, UP-algebras, and B-algebras, alongside others have validated fuzzy sets mathematically, thus proving their extensive applicability in abstract mathematical systems.