Generalized rough multiset via multiset ideals

Abstract

In this paper, ideals in the context of multisets on the lattice of all submultisets with the order relation as the multiset inclusion have been introduced. Moreover, generalization of rough multiset model by defining new multiset approximation operators in more general setting via multiset ideal has been presented. The concepts of lower and upper multiset approximations via multiset ideals have been mentioned. These new definitions decrease the upper multiset approximation and increase the lower multiset approximation and hence decreasing the boundary region and increasing the accuracy measure. Properties of these multiset approximations are studied and various examples are mentioned. Also, the comparison between the rough multiset approximations defined by Girish and John [11, 12] and the current multiset approximations has been presented. It’s therefore shown that the current definitions are more generally. Finally, the multiset topology induced by the present methods is finer than the multiset topology induced by the old method [11, 12].