Fuzzy Extended Filters oF MS-Algebras

Abstract

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

12pages