Rough set theory has been successfully applied to vague and uncertain data due to its approximation ability. Matroid is a sophisticated mathematical structure to provide a unifying abstract treatment for graph theory, linear algebra, and combinatorial optimization. In this paper, we redefine rough approximation operators throughmatroidal approaches and build a matroidal structure of rough set t...

The volume of data being generated nowadays is increasingly large. How to extract useful information from such data collections is an important issue. A promising technique is the Rough set theory, a new mathematical approach to data analysis based on classification of objects of interest into similarity classes which are indiscernible with respect to some features. This theory offers two funda...

A dialectical rough set theory focussed on the relation between roughly equivalent objects and classical objects was introduced in [1] by the present author. The focus of our investigation is on elucidating the minimal conditions on the nature of granularity, underlying semantic domain and nature of the general rough set theories (RST) involved for possible extension of the semantics to more ge...

The paper presents a transition from the crisp rough set theory to a fuzzy one, called Alpha Rough Set Theory or, in short, a-RST. All basic concepts or rough set theory are extended, i.e., information system, indiscernibility, dependency, reduction, core, de®nability, approximations and boundary. The resulted theory takes into account fuzzy data and allows the approximation of fuzzy concepts. ...

Rough set theory is an effective tool for data mining. According to the theory, a concept is definable if it can be written as a Boolean combination of equivalence classes induced from classification attributes. On the other hand, definability in logic has been explicated by Beth’s theorem. In this paper, we propose two data representation formalisms, called first-order data logic (FODL) and at...

In this paper, we address the problem of feature subset selection using rough set theory. We propose a scalable algorithm to find a set of reducts based on discernibility function, which is an alternative solution for the exhaustive approach. Our study shows that our algorithm improves the classical one from three points of view: computation time, reducts size and the accuracy of induced model.

One of the challenges in personalized e-learning research field is how to meet the unique learning strategies according to a learner’s personality characteristic. But a learner’s characteristic may have many attributes, and some of them have not equal value for personalized e-learning. This paper exploits the aspect to evaluate the important attributes, puts forward the concept of key personali...

We study generalized parameterized approximations, defined using both rough set theory and probability theory. The main objective is to study, for a given subset of the universe U , all such parameterized approximations, i.e., for all parameter values. For an approximation space (U,R), where R is an equivalence relation, there is only one type of such parameterized approximations. For an approx...

This paper reviews and compares theories of fuzzy sets and rough sets. Two approaches for the formulation of fuzzy sets are reviewed, one is based on many-valued logic and the other is based on modal logic. Two views of rough sets are presented, set-oriented view and operator-oriented view. Rough sets under set-oriented view are closely related to fuzzy sets, which leads to non-truth-functional...