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.
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