The paper presents an approach to data mining involving search for complete, or nearly complete, domain classifications in terms of attribute values. Our objective is to find classifications based on interacting attributes that provide a good characterization of the concept of interest by maximizing predefined quality criteria. The paper introduces the notion of the classification complexity an...

Abstract This article considers the problem of how to formulate a framework for the study of the nearness of tolerance rough sets (TRS). The solution to the problem stems from recent work on near sets and approach spaces as well as from the realisation that disjoint TRSs can be viewed in the context of approach merotopic spaces. A set of TRSs equipped with a distance function satisfying certain...

This paper further studies the fuzzy rough sets based on fuzzy coverings. We first present the notions of the lower and upper approximation operators based on fuzzy coverings and derive their basic properties. To facilitate the computation of fuzzy coverings for fuzzy covering rough sets, the concepts of fuzzy subcoverings, the reducible and intersectional elements, the union and intersection o...

Attribute reduction is viewed as an important preprocessing step for pattern recognition and data mining. Most of researches are focused on attribute reduction by using rough sets. Recently, Tsang et al. discussed attribute reduction with covering rough sets in the paper [E. C.C. Tsang, D. Chen, Daniel S. Yeung, Approximations and reducts with covering generalized rough sets, Computers and Math...

We show that any regular Kleene algebra defined on an algebraic lattice is isomorphic to a rough set Kleene algebra defined by a tolerance induced by an irredundant covering.