Generalized Rough Set Model on De Morgan Algebras

Abstract

By introducing the notion of similar topological open subsystem in De Morgan algebra, a pair of general rough approximations based on De Morgan algebra are defined. For the new generalized rough set model on De Morgan algebra (call it first type), some properties are given. Moreover, some uncertainty measures on bounded distribute lattice are introduced, and the relationship between those uncertainty measures and first type generalized rough set model on De Morgan algebra is discussed. Finally, the notion of similar closure subsystem of De Morgan algebra is introduced, and another rough set model on De Morgan algebra is constructed, call it second type generalized rough set model on De Morgan algebra.