Rough set theory is an important technique for knowledge discovery in databases, and its algebraic structure is part of the foundation of rough set theory. In this paper, we present the structures of the lower and upper approximations based on arbitrary binary relations. Some existing results concerning the interpretation of belief functions in rough set backgrounds are also extended. Based on ...

In this paper, the author presents the concept of topological space that must be used to show a relation between rough set and soft set. There are two main results presented; firstly, a construction of a quasi-discrete topology using indiscernibility (equivalence) relation in rough set theory is described. Secondly, the paper describes that a “general” topology is a special case of soft set. He...

This paper reviews probabilistic approaches to rough sets in granulation, approximation, and rule induction. The Shannon entropy function is used to quantitatively characterize partitions of a universe. Both algebraic and probabilistic rough set approximations are studied. The probabilistic approximations are defined in a decision-theoretic framework. The problem of rule induction, a major appl...

Decision-theoretic rough set theory is quickly becoming a research direction in rough set theory, which is a general and typical probabilistic rough set model with respect to its threshold semantics and decision features. However, unlike the Pawlak rough set, the positive region, the boundary region and the negative region of a decision-theoretic rough set are not monotonic as the number of att...

Worldwide, there has been a rapid growth in interest in rough set theory and its applications in recent years. Evidence of this can be found in the increasing number of high-quality articles on rough sets and related topics that have been published in a variety of international journals, symposia, workshops, and international conferences in recent years. In addition, many international workshop...

Granularity of knowledge attracted attention of many researchers recently. This paper concerns this issue from the rough set perspective. Granularity is inherently connected with foundation of rough set theory. The concept of the rough set hinges on classification of objects of interest into similarity classes, which form elementary building blocks (atoms, granules) of knowledge. These granules...

Attribute reduction is an important issue in rough set theory. This paper mainly studies attribute reduction of distributed incomplete decision information system (DIDIS). Firstly, the definition of rough set in DIDIS is developed. Next, an algorithm for attribute reduction of DIDIS is proposed. In the end, two groups of experiments are conducted to prove the effectiveness of the proposed metho...

In power system filed, to study the characteristics of the gas breakdown is essential and of importance in designing the protection of high voltage system as well as to the power system reliability. Hence, in this paper, the major purpose is to propose a refined mathematical approach based on core finding in rough set method and GM(h,N) method in grey system theory to find the priority of influ...