A commutative ring A with identity is called S-VSFT (S-very strong finite type), where \(S\subseteq A\) is a given multiplicative set, if for each ideal I of A, there exist \(s\in S\) , \(k\ge 1\) and a finitely generated ideal \(F\subseteq I\) such that \(sI^k\subseteq F\) (in this case I is called an S-VSFT ideal). In this paper, we give several generalizations of some results on VSFT rings. For instance, the ring A is S-VSFT if and only if each prime ideal of A is S-VSFT. Besides, we get some new results concerning the VSFT rings. In fact, we show that the ring A is S-VSFT if and only if the ring \(A(+)M\) is \(S(+)M\) -VSFT, where M is an A-module and \(A(+)M\) is idealization of M in A. Which turns out that A is VSFT if and only if \(A(+)M\) is VSFT. Many other results are also established.