The Characterization of L-Fuzzy Filters in Softened Distributive and Sectionally * Semilattices with certain applications

Abstract

The ideas of L-fuzzy filters, ideals, and semi lattices are examined in this work along with their characteristics. By defining the softened distributive semi lattice,we expand the notion of semi lattice to each section [0, 1] and investigate the requirements for a modular semi lattice to be softened distributive.Our research provides new insights into the structure and properties of fuzzy algebraic systems, with some potential applications in fuzzy logic. The main contributions of this study consists of, the creation of sufficient and required circumstances for softened distributive semi lattices.Proved that set of dense elements are a L-fuzzy filter. The paper investigates the properties of L-fuzzy filters and ideals in distributive semi lattices, providing a foundation for their applications. In this entire manuscript we denote semi lattice by the symbol S_∎.