Combinatorial Properties of Anti T-Subalgebra and Ideals on Fuzzy BP-Algebra with ᵵ -Norms

Introduction: We propose the -norm of the Anti-fuzzy T-subalgebra and the T-ideal of the BP-algebra, and investigate some of their properties in this work. In addition, we define properties of Cartesian products of Anti fuzzy T subalgebras and T-ideals of BP algebras. These are treated in detail along with other algebraic properties. Objectives: The primary objective of this study is to investigate the combinatorial properties of Anti T-subalgebras and T-ideals within the framework of fuzzy BP-algebras using ᵵ-norms. The research aims to explore and characterize their algebraic structures, including operations, interconnections, intersections, and Cartesian products. Methods: The concepts of t-norms can be applied to explore the algebraic properties of anti-fuzzy T-ideals and T-subalgebras within BP-algebras. These concepts are particularly relevant in formulating and proving theorems, lemmas, and illustrative examples related to the structure and behavior of such algebraic systems. Conclusions: In this study, we investigated the ȶ-norm of Anti-fuzzy T-subalgebras and T-ideals within the structure of BP-algebras and established several fundamental properties. We further introduced the concept of Cartesian products of Anti-fuzzy T-subalgebras and T-ideals, demonstrating key structural characteristics and interactions. The interconnection and intersection of these algebraic structures were also analyzed in depth, offering new insights into their theoretical behavior. The findings presented in this work provide a solid foundation for future extensions and generalizations. In particular, the notions developed here can be further explored in the context of intuitionistic Q-fuzzy sets, interval-valued Q-fuzzy sets, and Q-bipolar fuzzy sets, opening avenues for advanced research in generalized fuzzy algebraic systems.