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 A _i ∈ A is a set of attributes regarded as a context or background. Consequently, if there are n contexts in A, where A = {A ₁,..., A _n }, it provides n partitions. A given set of object, $X \subseteq U$ , 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.