An IFTS (X, [tau]) is said to be intuitionistic fuzzy countable weakly generalized compact if each countable intuitionistic fuzzy weakly generalized open cover of X has a finite sub cover for X.

An IFTS (X, [tau]) is said to be intuitionistic fuzzy nearly weakly generalized compact if each intuitionistic fuzzy weakly generalized closed cover of X has a finite sub cover.

An IFTS (X, [tau]) is said to be intuitionistic fuzzy nearly weakly generalized Lindelof if each intuitionistic fuzzy weakly generalized closed cover of X has a countable sub cover for X.

An IFTS (X, [tau]) is said to be intuitionistic fuzzy nearly countable weakly generalized compact if each countable intuitionistic fuzzy weakly generalized closed cover of X has a finite sub cover for X.

An IFTS (X, [tau]) is said to be intuitionistic fuzzy almost weakly generalized compact if each intuitionistic fuzzy weakly generalized open cover of X has a finite sub cover the closure of whose members cover X.

An IFTS (X, [tau]) is said to be intuitionistic fuzzy almost weakly generalized Lindelof if each intuitionistic fuzzy weakly generalized open cover of X has a countable sub cover the closure of whose members cover X.

An IFTS (X, [tau]) is said to be intuitionistic fuzzy almost countable weakly generalized compact if each countable intuitionistic fuzzy weakly generalized open cover of X has a finite sub cover the closure of whose members cover X.

A crisp subset B of an IFTS (X, [tau]) is said to be intuitionistic fuzzy weakly generalized compact if B is intuitionistic fuzzy weakly generalized compact as intuitionistic fuzzy subspace of X.

Let f : (X, [tau]) [right arrow] (Y, [sigma]) be an IFWG continuous mapping from an IFTS (X, [tau]) onto an IFTS (Y, [sigma]).

Let f : (X, [tau]) [right arrow] (Y, [sigma]) be an IF quasi WG continuous mapping from an IFTS (X, [tau]) onto an IFTS (Y, [sigma]).

Let f : (X, [tau]) [right arrow] (Y, [sigma]) be an IF perfectly WG continuous mapping from an IFTS (X, [tau]) onto an IFTS (Y, [sigma]).

If f : (X, [tau]) [right arrow] (Y, [sigma]) is an IFWG irrresolute mapping and an intuitionistic fuzzy subset B of an IFTS (X, [tau]) is intuitionistic fuzzy weakly generalized compact relative to an IFTS (X, [tau]), then the image f (B) is intuitionistic fuzzy weakly generalized compact relative to (Y, [sigma]).