In this paper we introduce and study maximal fuzzy P-spaces where P is
fuzzy Lindelof, fuzzy countably compact, fuzzy compact, fuzzy lightly
compact or fuzzy strongly compact. Characterizations are given for ma
ximal fuzzy P-spaces where P is fuzzy Lindelof, fuzzy countably compac
t, fuzzy compact, or fuzzy strongly compact. Necessary condition is gi
ven for maximal fuzzy lightly compact spaces and fuzzy connected space
s.