Annals of Communications in Mathematics

AbstractIn this article, the concepts of interior, weak-interior and quasi-interior filters in a quasi-ordered Γ-semigroup are introduced and recognize some of their fundamental properties. In addition to the above, the relationships between these three classes of filters in quasi-ordered Γ-semigroups are considered. One of the specifics in this analysis, among others, is that the requirement that a filter in a quasi-ordered Γ-semigroup S has to be a sub-semigroup in S is omitted. Instead of this requirement in the determination of these three classes of filters the consistency requirement is incorporated

AbstractThis paper introduces a novel approach to the study of filters in BL-algebras by leveraging the principles of bipolar fuzzy set theory and investigating some of their properties. Filters are essential in the structural analysis of BL-algebras, affecting their properties and applications across various fields. Moreover, Bipolar-valued fuzzy filters generated by a fuzzy set are discussed. By integrating bipolar fuzzy set concepts, we provide a new framework that enhances the representation of uncertainty and vagueness inherent in filter operations.  We explore the foundational aspects of bipolar fuzzy sets and demonstrate their applicability in defining and characterizing filters within BL-algebras. Our findings highlight the potential of bipolar fuzzy set theory to enrich the understanding of filters in BL-algebras.