In this paper we consider new weak and stronger forms of fuzzy irresolute and fuzzy semi-closure via the concept Fsg-closed sets which we call Fap-irresolute maps, Fap-semi-closed maps and contra-fuzzy irresolute and we use it to obtain several results in the literature concerning the preservation of fuzzy sg-closed sets and to abtain also a characterization of fuzzy semi-T1/2 spaces