Fuzzy primely filters in BL-algebras

Abstract

This study introduces and rigorously examines the concept of fuzzy primely filters (FPYFs) in BL-algebras, marking a significant advancement in the field. The investigation extends beyond conceptualization to elucidate the complex interrelationships between FPYFs and established fuzzy filter classes within the BL-algebraic framework. Through comprehensive analysis, we uncover intricate connections and potential hierarchical structures among these diverse filter types. Our findings not only expand the theoretical landscape of BL-algebras but also provide a robust foundation for further exploration of fuzzy filter relationships. This research contributes to a deeper understanding of the algebraic structures underpinning fuzzy logic systems, offering new insights into the fundamental properties of BL-algebras and their associated filters. Furthermore, by leveraging the concept of the complement set, we embark on a rigorous investigation into the interplay between FPYFs and fuzzy prime ideals (FPEIs). This investigation seeks to elucidate the nature of their interaction and potential implications for the broader theory of BL-algebras.