In this chapter, the basics of the rough set approach are presented, and an outline of an exemplary processor structure is given. The organization of a simple processor is based on elementary rough set granules and dependencies between them. The rough set processor (RSP) is meant to be used as an additional fast classification unit in ordinary computers or as an autonomous learning machine. In ...

This paper reviews and discusses generalizations of Pawlak rough set approximation operators in mathematical systems, such as topological spaces, closure systems, lattices, and posets. The structures of generalized approximation spaces and the properties of approximation operators are analyzed.

Rough set theory provides an effective tool to deal with uncertain, granular, and incomplete knowledge in information systems. Matroid theory generalizes the linear independence in vector spaces and has many applications in diverse fields, such as combinatorial optimization and rough sets. In this paper, we construct a matroidal structure of the generalized rough set based on a tolerance relati...

This paper presents a general framework for the study of rough set approximation operators in fuzzy environment in which both constructive and axiomatic approaches are used. In constructive approach, a pair of lower and upper generalized fuzzy rough (and rough fuzzy, respectively) approximation operators is first defined. The representations of both fuzzy rough approximation operators and rough...

In order to discover interesting patterns and dependencies in data, an approach based on rough set theory can be used. In particular, Dominance-based Rough Set Approach (DRSA) has been introduced to deal with the problem of ordinal classification with monotonicity constraints (also referred to as multicriteria classification in decision analysis). However, in real-life problems, in the presence...

Rough sets are efficient for data pre-processing in data mining. Matroids are based on linear algebra and graph theory, and have a variety of applications in many fields. Both rough sets and matroids are closely related to lattices. For a serial and transitive relation on a universe, the collection of all the regular sets of the generalized rough set is a lattice. In this paper, we use the latt...

A rough set approach for attribute reduction is an important research subject in data mining and machine learning. However, most attribute reduction methods are performed on a complete decision system table. In this paper, we propose methods for attribute reduction in static incomplete decision systems and dynamic incomplete decision systems with dynamically-increasing and decreasing conditiona...

An information table can change over time in several different ways: objects enter/exit the system, new attributes are considered, etc. As a consequence rough set instruments also change. At first, we recall a classification of dynamic increase of information with respect to three different factors: objects, attributes, values. Then, the corresponding changes in rough sets are discussed. Result...

Granular computing is a new information processing method. Many models and methods of granular computing have been proposed and studied. Nowadays, the granular computing has been appeared in many areas of information processing. In this paper, a study of the model of granular computing on Binary Relations based on Generalized Rough Set is presented. We hope to expand the range of application of...

In order to discover interesting patterns and dependencies in data, an approach based on rough set theory can be used. In particular, Dominance-based Rough Set Approach (DRSA) has been introduced to deal with the problem of multicriteria classification. However, in real-life problems, in the presence of noise, the notions of rough approximations were found to be excessively restrictive, which l...