Rough Sets and Rough Logic: A KDD Perspective
Zdzisław Pawlak, Lech Polkowski, Andrzej Skowron · Studies in fuzziness and soft computing · 2000
Basic ideas of rough set theory were proposed by Zdzislaw Pawlak [90, 91] in the early 1980’s. In the ensuing years, we have witnessed a systematic, world-wide growth of interest in rough sets and their applications. There are numerous areas of successful applications of rough set software systems [101]. Many interesting case studies are reported (for references see e.g., [100, 101], [87] and the bibliography in these books, in particular [19], [46], [57], [132], [1461).The main goal of rough set analysis is induction of approximations of concepts. This main goal is motivated by the basic fact, constituting also the main problem of KDD, that languages we may choose for knowledge description are incomplete with respect to expressibility. A fortiori, we have to describe concepts of interest (features, properties, relations etc.) known not completely but by means of their reflections (i.e., approximations) in the chosen language. The most important issues in this induction process are: construction of relevant primitive concepts from which approximations of more complex concepts are assembled, measures of inclusion and similarity (closeness) on concepts, construction of operations producing complex concepts from the primitive ones. Basic tools of rough set approach are related to concept approximations. They are defined by approximation spaces. For many applications, in particular for KDD problems, it is necessary to search for relevant approximation spaces in the large space of parameterized approximation spaces. Strategies for tuning parameters of approximation spaces are crucial for inducing concept approximations of high quality.Methods proposed in rough set approach are kin to general methods used to solve Knowledge Discovery and Data Mining (KDD) problems like feature selection, feature extraction (e.g., discretization or grouping of symbolic value), data reduction, decision rule generation, pattern extraction (templates, association rules), or decomposition of large data tables. In this Chapter we examine rough set contributions to Knowledge Discovery from the perspective of KDD as a whole.This Chapter shows how several aspects of the above problems are solved by the classical rough set approach and how they are approached by some recent extensions to the classical theory of rough sets. We point out the role of Boolean reasoning in solving discussed problems. Rough sets induce via its methods a specific logic, which we call rough logic. We also discuss rough logic and related logics from a wider perspective of logical approach in KDD. We show some relationships between these logics and potential directions for further research on rough logic.