# Fuzzy n-fold obstinate and maximal (pre)filters of EQ-algebras

Document Type : Original Article

Author

Department of Mathematics Faculty of Mathematical Sciences Alzahra University Tehran Iran

Abstract

In this paper, we defined the concepts of fuzzy $n$-fold obstinate (pre)filter and maximal fuzzy (pre)filter of $EQ$-algebras and discussed the properties of them. We show that every maximal fuzzy (pre)filter of $\mathcal{\LomE}$ is normalized and takes only the values $\{0, 1\}$. Also we show that in good $EQ$-algebra, if $\m$ is a normalized fuzzy (pre)filter of $\mathcal{\LomE}$, then $\m$ is a fuzzy $n$-fold obstinate (pre)filter of $\mathcal{\LomE}$ if and only if every normalized fuzzy (pre)filter of quotient algebra $\mathcal{\LomE}/\m$ is a fuzzy $n$-fold obstinate (pre)filter of $\mathcal{\LomE}/\m$.
Also, we verify relation between fuzzy obstinate $n$-fold (pre)filters and other fuzzy (pre)filters of $EQ$-algebras.

Keywords