TL;DR: It has been proved that the reduct of a covering is the minimal covering that generates theSame covering lower approximation or the same covering upper approximation, so this concept is also a technique to get rid of redundancy in data mining.
TL;DR: It is shown that some of the properties of Pawlak's rough set theory are special instances of those of MGRS, and several important measures are presented, which are re-interpreted in terms of a classic measure based on sets, the Marczewski-Steinhaus metric and the inclusion degree measure.
TL;DR: An information measure is proposed to computing discernibility power of a crisp equivalence relation or a fuzzy one, which is the key concept in classical rough set model and fuzzy-rough set model, and a general definition of significance of nominal, numeric and fuzzy attributes is presented.
TL;DR: It is proved that for some special thresholds, β lower distribution reduct is equivalent to the maximum distribution reduction reduct, whereas β upper distribution reduCT is equivalents to the possible reduct.
TL;DR: The rough sets hybridization with fuzzy sets, neural network and metaheuristic algorithms have been reviewed and the performance analysis of the algorithms has been discussed in connection with the classification.
Abstract: A rough set theory is a new mathematical tool to deal with uncertainty and vagueness of decision system and it has been applied successfully in all the fields. It is used to identify the reduct set of the set of all attributes of the decision system. The reduct set is used as preprocessing technique for classification of the decision system in order to bring out the potential patterns or association rules or knowledge through data mining techniques. Several researchers have contributed variety of algorithms for computing the reduct sets by considering different cases like inconsistency, missing attribute values and multiple decision attributes of the decision system. This paper focuses on the review of the techniques for dimensionality reduction under rough set theory environment. Further, the rough sets hybridization with fuzzy sets, neural network and metaheuristic algorithms have also been reviewed. The performance analysis of the algorithms has been discussed in connection with the classification.