One of the important basic notions in topological spaces is closed sets as well as open sets. Levine (resp. Jankovic et al. (Am. Math. Monthly 97:295–310, 1990)) introduced the notion of g-closed (resp. \(\tau ^{*}\) -closed) sets as two generalizations of closed sets. In this paper, we define a new closed set type called \(*pIg\) -closed and obtained that it is weaker than \(\tau ^{*}\) -closed and stronger than \(*Ig\) -closed. We give several properties of it by studing densely. Besides we introduce notion of \(*pIg\) -open as complement of \(*pIg\) -closed. Of course since it is a a new type open sets, so we state some basic features. We answered the question of when to preserve \(*pIg\) -closed set by using the image of the ideal under the function and preserving its inverse image.