This paper presents and compares two views of the theory of rough sets. The operator-oriented view interprets rough set theory as an extension of set theory with two additional unary operators. Under such a view, lower and upper approximations are related to the interior and closure operators in topological spaces, the necessity and possibility operators in modal logic, and lower and upper appr...

This paper presents and compares two views of the theory of rough sets. The operator-oriented view interprets rough set theory as an extension of set theory with two additional unary operators. Under such a view, lower and upper approximations are related to the interior and closure operators in topological spaces, the necessity and possibility operators in modal logic, and lower and upper appr...

The notion of a rough set was originally proposed by Pawlak [Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences 11 (5) (1982) 341–356]. Later on, Dubois and Prade [D. Dubois, H. Prade, Rough fuzzy sets and fuzzy rough sets, International Journal of General System 17 (2–3) (1990) 191–209] introduced rough fuzzy sets and fuzzy rough sets as a generalization of rough...

Rough set is approximate representation of a crisp set. Rough set theory provides an approach to approximation of sets that leads to useful forms of granular computing. Several applications have revealed the need to extend the traditional rough set approach. A special place among various extensions is taken by the approach that replaces the relation based on equivalence with a tolerance relatio...

The Rough Set (RS) theory can be considered as a tool to reduce the input dimensionality and to deal with vagueness and uncertainty in datasets. Over the years, there has been a rapid growth in interest in rough set theory and its applications in artificial intelligence and cognitive sciences, especially in research areas such as machine learning, intelligent systems, inductive reasoning, patte...

Rough set theory introduced by Pawlak [8] is based on equivalence relations. The definition of basic rough sets depends upon a single equivalence relation defined on the universe or several equivalence relations taken one each taken at a time. In the view of granular computing, classical rough set theory is based upon single granulation. The basic rough set model was extended to rough set model...

The theory rough set successfully implemented diberbagai sector , but rough set model classical can only associated with the data complete and set of data in symbolic form ( Jianhua , dai , 2013 ) . Research by adopting the theory rough set conducted in attribute numerical and the value of an attribute lost ( Jerzy w , Grzymala-Buse and Zdzislaw S , Hippe , Nov .2011 ) .In this research discuss...

Knowledge Discovery in Databases (KDD) has evolved into an important and active area of research because of theoretical challenges and practical applications associated with the problem of discovering (or extracting) interesting and previously unknown knowledge from very large real-world databases. Rough Set Theory (RST) is a mathematical formalism for representing uncertainty that can be consi...

The rough set theory approximates a concept by three regions, namely, the positive, boundary and negative regions. Rules constructed from the three regions are associated with different actions and decisions, which immediately leads to the notion of three-way decision rules. A positive rule makes a decision of acceptance, a negative rule makes a decision of rejection, and a boundary rule makes ...

The concept of the rough set was originally proposed by Pawlak as a formal tool for modelling and processing incomplete information in information systems, then in 1990, Dubois and Prade first introduced the rough fuzzy sets and fuzzy rough sets as a fuzzy extension of the rough sets. The aim of this paper is to present a new extension of the rough set theory by means of integrating the classic...