Lattices defined by multigranular rough sets

Abstract

One way to view the multigranular rough set model is that the assessment of more experts are considered when determining the approximations of a set, instead of a single equivalence relation expressing the indiscernibility of the objects. There are two approaches for modeling this: the optimistic and the pessimistic multigranular rough set models. In this paper, we analyze both approaches from a lattice-theoretic point of view. We generalize existing results for two equivalence relations (two experts) to n equivalence relations, completing them with additional findings. We also characterize the order structures of optimistic and pessimistic rough sets and determine when they form complete, or even completely distributive lattices. Additionally, we examine the properties of the Dedekind-MacNeille completion of the poset of optimistic multigranular rough sets. Some applications for information tables and for recommendation theory are also presented.