Rough Sets

Abstract

Rough sets — a concept of granular computing introduced by Zdzislaw Pawlak (Pawlak, 1982, Pawlak, 1984, Pawlak, 1986, Pawlak, 1991, Pawlak, 1999) are concerned about the notion of roughness. It inherently arises when we are interested in describing concepts in the language of some generic knowledge-based entities and is intimately linked with an idea of indiscernibility between elements (more formally, an indiscernibility relation). In other words, we may treat rough sets as a framework in which we represent concepts in the setting of indiscernibility relations. It is convenient to cast rough sets and their underlying methodology in the general two-phase development process as being usually applied in practice. First, we consider (assume) a collection of generic descriptors that are treated as essential blocks whose distinction and usage is central to all cognitive activities going on in the problem under consideration. Second, we express any new concept X (either emerging in the problem or being communicated by the external environment) in the language of the generic descriptors we have identified in the first phase. Evidently, an expression of X carried out by means of these descriptors may not be perfect (and this is usually the case), hence we end up with some “roughness” of the characterization of X.