In Rough Set Theory, dependency in the knowledge base is an important aspect when drawing inferences about the world. Rough set (inexact set) is defined by using a fixed binary relation (equivalence relation, tolerance relation, similarity relation, etc) to analyze vague, imprecise, inexact problems, which satisfy many interesting properties. The neighborhood based rough set theory is an extens...

Rough set theory is an important technique in knowledge discovery in databases. Classical rough set theory proposed by Pawlak is based on equivalence relations, but many interesting and meaningful extensions have been made based on binary relations and coverings, respectively. This paper makes a comparison between covering rough sets and rough sets based on binary relations. This paper also foc...

Rough set theory is a useful and effective tool to cope with granularity and vagueness in information system and has been used in many fields. However, it is hard to get the reduct of a covering in rough sets. This paper attempts to get the reduct of a covering at a high speed in theory. It defines upset and downset based on a poset in a covering, studies the relationship between reducible elem...

Covering approximation spaces are a generalization of equivalence-based rough set theories. In this paper, we will consider twelve types of covering based approximation operators by combining four types of covering lower approximation operators and three types of covering upper approximation operators. Then, we will study the properties of these new pairs and show they have most of the common p...

Covering based Rough Sets are an important generalization of Rough Set Theory. Basically, they replace the partition generated from an equivalence relation by a covering. In this context many approximation operators can be defined [16, 26, 27, 28, 34]. In this paper we want to discover relationships among approximation operators defined from neighborhoods. We use the concepts of duality, adjoin...

Covering-based rough sets provide an efficient theory to deal with covering data which widely exist in practical applications. Boolean matrix decomposition has been widely applied to data mining and machine learning. In this paper, three types of existing covering approximation operators are represented by boolean matrices, and then they are used to decompose into boolean matrices. First, we de...

Adopting Zakowski’s upper approximation operator C and lower approximation operator C, this paper investigates granularity-wise separations in covering approximation spaces. Some characterizations of granularity-wise separations are obtained by means of Pawlak rough sets and some relations among granularitywise separations are established, which makes it possible to research covering approximat...