Multi-rough sets based on multi-contexts of attributes

Abstract

Rough set deals with crisp granularity of objects given a data table called information system as a pair I = (U,A), where U is a universal set of objects and A is a non-empty finite set of attributes. We may consider A as a set of contexts of attributes, where Ai ∈ A is a set of attributes regarded as a context or background. Consequently, if there are n contexts in A, where A = {A1,…, An}, it provides n partitions. A given set of object, X ⊆ U, may then be represented into n pairs of lower and upper approximations denoted as multi-rough sets of X. Some properties and operations are proposed and examined.