L-ideals and rough sets based on L-ideals

摘要

Let D be a distributive lattice, and let L be a frame. In this article, we introduce the notion of L-ideals of D. We show that the set of all L-ideals of D is a distributive lattice, and some essential properties of this lattice are studied. Also, we discuss some special elements of this lattice. Moreover, we define a novel congruence relation for the concept of L-ideal of D. Finally, we study some properties of rough sets inherited from the congruence relation.