Fuzzy Extended Filters oF MS-Algebras

TL;DR

This paper introduces and studies extended and strong fuzzy filters within MS-algebras, exploring their properties, characterizations, and homomorphisms to advance the understanding of fuzzy filter structures.

Contribution

It presents new concepts of extended and strong fuzzy filters in MS-algebras, providing their properties, characterizations, and homomorphism behaviors.

Findings

Properties of extended fuzzy filters are established.

Characterizations using dense elements are provided.

Homomorphism behaviors of the filters are analyzed.

Abstract

In this article, for an $\emph{MS}$- algebra and a fuzzy filter $\chi $, the concept of extended fuzzy filter of $\chi$ is presented, notated by $ \Upsilon_{\chi,W}$ with $W \subseteq \mathcal{L}$. The features of $\Upsilon_{\chi,W}$ are investigated. Furthermore, the strong fuzzy filter is introduced, donated by $\Omega_{\chi,W}$. Many properties are studied. Characterisation of both $ \Upsilon_{\chi,W}, \Omega_{\chi,W}$ are clarified by using the notion of dense elements with respect to a fuzzy filter. The homomorphisms of both $\Upsilon_{\chi,W}$ and $\Omega_{\chi,W}$ are triggered.