A STRONG FORM OF GENERALIZED CLOSED SET IN A FUZZY TOPOLOGICAL SPACE

In this paper a strong form of fuzzy generalized closed set, viz., $fg^{*}s$-closed set is introduced and studied. With the help of this newly defined set, a new type of idempotent operator is introduced. Using this operator as a basic tool, here we introduce and study $fg^{*}s$-open and $fg^{*}s$-closed functions the class of which are strictly larger than that of fuzzy open (resp, $fg$-open) and fuzzy closed (resp., $fg$-closed) functions respectively and weaker than that of $fg\delta$-open and $fg\delta$-closed functions respectively. In the last section we introduce $fg^{*}s$-$T_{2}$-space the class of which is strictly larger than that of fuzzy $T_{2}$-space and some applications of $fg^{*}s$-open function are established here.