In  Dündar introduced the notion of rough I and obtained two criteria for rough I 2 -convergence. In the present paper we 2 -convergenceintroduce some new rough ideal convergent sequence spaces of Musielak-Orlicz functions and four dimensional bounded-regular matrices. We study some topological and algebraic properties of these spaces. We also establish some inclusion relations between these spaces. Finally, we examine that these spaces are normal as well as monotone and sequence algebras. © 2018, Sciendo. All rights reserved.