Abstract
In this paper, a condition which ensures the existence of fuzzy simply open sets in a fuzzy $P$- space is obtained. It is established that disjoint fuzzy $G_{\delta}$-sets in a fuzzy $P$-space are fuzzy cs dense sets. A condition for a fuzzy strongly irresolvable and fuzzy globally disconnected space to become a fuzzy $P$-space is obtained. It is established that fuzzy hyperconnected and fuzzy $P$-space is a fuzzy D-Baire space. It is obtained that fuzzy extremally disconnected, fuzzy strongly irresolvable and fuzzy $P$-space is a fuzzy semi-$P$ space and fuzzy hyperconnected and fuzzy $P$-space does not have disjoint fuzzy $G_{\delta}$-sets.
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