Neutrosophic UP (BCC)-Subalgebras of Several Types: A Threshold-Based Analysis in UP (BCC)-Algebras

This study provides an extensive investigation into neutrosophic subalgebras within the context of BCC-algebras, establishing a new framework for their classification. By utilizing neutrosophic set theory—a generalization of fuzzy and intuitionistic fuzzy sets—the authors systematically examine three distinct types of neutrosophic subalgebras based on varying membership relations and their hybrid forms. A significant contribution of this research is the definition of rigorous conditions under which specific neutrosophic subsets qualify as algebraic subalgebras. This is achieved through a threshold-based analysis using specific parameters to define the boundaries of truth, indeterminacy, and falsity. The paper derives algebraic characterizations for these structures and validates them through both illustrative examples and counterexamples. Notably, the research demonstrates that certain subsets exhibit subalgebraic properties only under specific threshold constraints, thereby extending traditional results found in fuzzy algebraic structures. These findings strengthen the theoretical groundwork for neutrosophic algebraic systems and provide a robust tool for modeling uncertainty in logical algebras and decision-making processes.