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...

Rough set theory provides a useful mathematical concept to draw tends to serve well for data mining applications whereas the predictive model. The rough set toolkit for analysis of data (ROSETTA), which is an advanced machine learning algorithms for data mining tasks implemented in Java (33). Therefore, this paper presents the RoughSets package that allows researchers. Zdzislaw Pawlak, Rough Se...

The roughness of a rough set arises from the existence of its boundary region. In such a boundary region, each object has a non-zero rough membership degree. When an object’s rough membership degree is regarded as its fuzzy membership degree, a rough set can induce a fuzzy set. This relationship motivates us to assert that there may exist some inherent relations between the roughness of a rough...

Since upper and lower approximations could be induced from the rough set structures, rough sets are considered as approximations. The concept of fuzzy rough sets was proposed by replacing crisp binary relations with fuzzy relations by Dubois and Prade. In this paper, we introduce and investigate some properties of intuitionistic fuzzy rough approximation operators and intuitionistic fuzzy relat...

• On Irreducible Descriptive Sets of Attributes for Information Systems Mikhail Moshkov, Andrzej Skowron, Zbigniew Suraj • Dominance-Based Rough Set Approach and Bipolar Abstract Rough Approximation Spaces Salvatore Greco, Benedetto Matarazzo, Roman Słowinski • Paraconsistent Logic Programs with FourValued Rough Sets Jan Małuszynski, Andrzej Szałas, Aida Vitória • An Equivalent Definition of Ro...

Distance provides a comprehensible perspective for characterizing the difference between two objects in a metric space. There are many measures which have been proposed and applied for various targets in rough set theory. In this study, through introducing set distance and partition distance to rough set theory, we investigate how to understand measures from rough set theory in the viewpoint of...

Clustering is a standard approach in analysis of data and construction of separated similar groups. The most widely used robust soft clustering methods are fuzzy, rough and rough fuzzy clustering. The prominent feature of soft clustering leads to combine the rough and fuzzy sets. The Rough Fuzzy C-Means (RFCM) includes the lower and boundary estimation of rough sets, and fuzzy membership of fuz...

The paper presents a new hybridization methodology involving Neural, Fuzzy and Rough Computing. A Rough Sets based approximation technique has been proposed based on a certain Neuro – Fuzzy architecture. A New Rough Neuron composition consisting of a combination of a Lower Bound neuron and a Boundary neuron has also been described. The conventional convergence of error in back propagation has b...

Covering-based rough sets is an extension of rough sets and it is based on a covering instead of a partition of the universe. Therefore it is more powerful in describing some practical problems than rough sets. However, by extending the rough sets, covering-based rough sets can increase the roughness of each model in recognizing objects. How to obtain better approximations from the models of a ...