1. INTRODUCTION: Set theory as a branch of human endeavour was developed by the efforts of many mathematicians [ Kam ]. Such a theory found many applications in science, technology and other fields. In an effort to capture uncertainity in human reasoning, Zadeh formulated and studied the theory of fuzzy sets. The theory of fuzzy sets found applications in many branches of science and technology...

In this paper, two new operators are introduced for the rough set theory. Using them, two inequalities well known in the rough set theory can now be modified to become equalities. With this change, no information will be lost in the new expressions. Hence, many properties in rough set theory can be improved and in particular, the union, the intersection, and the complement operations can be red...

$L$-fuzzy rough sets are extensions of the classical rough sets by relaxing theequivalence relations to $L$-relations. The topological structures induced by$L$-fuzzy rough sets have opened up the way for applications of topological factsand methods in granular computing. In this paper, we firstly prove thateach arbitrary $L$-relation can generate an Alexandrov $L$-topology.Based on this fact, w...

In this paper, the main techniques of inductive machine learning are united to the knowledge reduction theory based on rough sets from the theoretical point of view. And then the Monk’s problems are resolved again employing rough sets. As far as accuracy and conciseness are concerned, the learning algorithms based on rough sets have remarkable superiority to the previous methods.

We study properties of rough sets, that is, approximations to sets of records in a database or, more formally, to subsets of the universe of an information system. A rough set is a pair hL; U i such that L; U are deenable in the information system and L U. In the paper, we introduce a language, called the language of inclusion-exclusion, to describe incomplete speciications of (unknown) sets. W...

This paper presents a general framework for the study of rough fuzzy sets in which fuzzy sets are approximated in a crisp approximation space. By the constructive approach, a pair of lower and upper generalized rough fuzzy approximation operators is first defined. The rough fuzzy approximation operators are represented by a class of generalized crisp approximation operators. Properties of rough...

The theory of rough sets is an extension of set theory with two additional unary set-theoretic operators deened based on a binary relation on the universe. These two operators are related to the modal operators in modal logics. By exploring the relationship between rough sets and modal logics, this paper proposes and examines a number of extended rough set models. By the properties satissed by ...

Application of intelligent methods in industry become a very challenging issue nowadays and will be of extreme importance in the future. Intelligent methods include, fuzzy sets neural networks genetics algorithms and others techniques known as soft computing. No doubt rough set theory can also contribute essentially to this domain. In this paper basic ideas of rough set theory are presented and...

Fuzzy sets and rough sets address two important, and mutually orthogonal, characteristics of imperfect data and knowledge: while the former allow that objects belong to a set or relation to a given degree, the latter provide approximations of concepts in the presence of incomplete information. In this chapter, we demonstrate how these notions can be combined into a hybrid theory that is able to...

In many Knowledge Discovery applications, finding outliers is more interesting than finding inliers in a dataset. The perception of outliers is rare cases in dataset in which is being described as abnormal data in the information table. Outliers detections are applied in many important applications like fraud detection systems to uncover the suspicious objects which may have important knowledge...