This paper deals with a new type of fuzzy generalized version of closed sets, called fğ-closed sets, which is already defined in [16]. Again the mutual relationships of this class of sets with other classes defined in [3, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16] are established. Then a new type of closure operator, called fğ-closure operator, is introduced and it is proved that this is an idempotent operator. With the help of this operator, fğ-open, fğ-closed, fğ-continuous and fğ-irresolute functions are introduced and characterized. Afterwards, fğ-regular, fğ-normal, fğ-compact, fğ-T2-spaces are introduced and characterized. Lastly, applications of the above mentioned functions on these spaces are given.