Rough sets perspective on data and knowledge

TLDR: This chapter outlines the basic notions of rough sets, especially those that are related to knowledge extraction from data and illustrative examples of applications of this general scheme to inducing from data various forms of knowledge.

Abstract: Rough set theory was proposed by Zdzislaw Pawlak (1982, 1991) in the early 1980s. Since then we have witnessed a systematic, worldwide growth of interest in rough set theory and its applications. The rough set approach has been introduced to deal with vague or imprecise concepts, to derive knowledge from data, and to reason about knowledge derived from data. In the first part of this chapter we outline the basic notions of rough sets, especially those that are related to knowledge extraction from data. Searching for knowledge is usually guided by some constraints (Langley et al., 1987). A wide class of such constraints can be expressed by discernibility of objects. Knowledge derived from data by the rough set approach consists of different constructs. Among them there are reducts, which are the central construct in the rough set approach, different kinds of rules (such as decision rules or association rules), dependencies, and patterns (templates), or classifiers. The reducts are of special importance since all other constructs can be derived from different kinds of reducts using the rough set approach. Strategies for searching reducts apply Boolean (propositional) reasoning (Brown, 1990), since the constraints (e.g., constraints related to the discernibility of objects) are expressible by propositional formulas. Moreover, using Boolean reasoning, minimal description-length data models (Mitchell, 1997; Rissanen, 1978) can be induced since they correspond to constructs of Boolean functions called prime implicants (or their approximations). The second part of this chapter includes illustrative examples of applications of this general scheme to inducing from data various forms of knowledge.