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The theory of rough sets is an extension of the set theory, for the study of intelligent systems characterized by insufficient and incomplete information. Since proposed by Pawlak, rough sets have evoked a lot of research. Theoretic study has included algebra aspect of rough sets. In paper [1] the concept of rough group and rough subgroup was introduced, but with some deficiencies remaining. In this paper, we intend to make up for these shortages, improve definitions of rough group and rough subgroup, and prove their new properties.

The aim of this paper is to compare concept lattices and approximation spaces. For this purpose general approximation spaces are introduced. It is shown that formal contexts and information systems on one hand and general approximation spaces on the other could be mutually represented e.g. for every information system exists a general approximation space such that both structures determines the same indiscernibility relation. A close relationship between Pawlak’s approximation spaces and general approximation spaces also holds: for each approximation space exists a general approximation space such that both spaces determine the same definable sets. It is shown on the basis of these relationships that an extent of the every formal concept is a definable set in some Pawlak’s approximation space. The problem when concept lattices are isomorphic to algebras of definable sets in approximation spaces is also investigated.

This paper studies some matrix properties of rough sets over an arbitrary Boolean algebra, and their comparison with the corresponding ones of Pawlak’s rough sets, a tool for data mining. The matrix representation of the lower and upper approximation operators of rough sets is given. Matrix approach provides an explicit formula for computing lower and upper approximations. The lower and upper approximation operators of column vector over an arbitrary Boolean algebra are defined. Finally, a set of axioms is constructed to characterize the upper approximation operator of column vector.

In this paper, we introduce the notion of generalized algebraic lower (upper) approximation operator and give its characterization theorem. That is, for any atomic complete Boolean algebra with the set of atoms, a map is an algebraic lower approximation operator if and only if there exists a binary relation on such that = , where is the lower approximation defined by the binary relation . This generalizes the results given by Yao.

Many researchers study rough sets from the point of view of description of the rough set pairs(a rough set pair is also called a rough set), i.e. <lower approximation set, upper approximation set>. An important result is that the collection of rough sets of an approximation space can be made into a regular double Stone algebra. In this paper, a logic for rough sets, i.e., the sequent calculus corresponding to rough double Stone algebra, is proposed. The syntax and semantics are defined. The soundless and completeness are proved.

In the paper a greedy algorithm for construction of partial tests is considered. Bounds on minimal cardinality of partial reducts are obtained. Results of experiments with software implementation of the greedy algorithm are described.

In practice, many datasets are shared among multiple users. However, different users may desire different knowledge from the datasets. It implies that we need to provide a specification which mines different solutions from the dataset according to the semantic of requirements. Attribute order is a better approach to describing the semantic. A algorithm based on attribute order has been presented in [1]. Because of its completeness for and its unique output for a given attribute order, this algorithm can be regarded as a mapping from the attribute orders set to the set. This paper investigates the structure of attribute orders set for the . The second attribute theorem, which can be used to determine the range of attribute orders with the same for a given attribute order, has been proved in [2]. Consequently, key to use the second attribute theorem is how to find the second attributes with the largest subscript for application in an efficient way. This paper therefore presents a method based on the tree expression to fulfill the above task.

A core in information system is a set of attributes globally necessary to distinct objects from different decision classes (i.e., the intersection of all reducts of the information system). A notion of a pairwise core (2-core), which naturally extends the definition of a core into the case of pairs of attributes is presented. Some useful features concerned with the graph representation of pairwise cores are discussed.

The paper presents also practical application of the notion of 2-core. It is known that a core (if exists) may be used to improve the reduct finding methods, since there exist polynomial algorithms for core construction. The same may be proven for a 2-core, which may be also used for estimation of minimal reduct size.

Data preprocessing is an essential step of the KDD process. It makes it possible to extract useful information from data. We propose two coefficients which respectively study the informational contribution of initial data in supervised learning and the intrinsic structure of initial data in not supervised one. These coefficients are based on Kappa coefficient. The confrontation of these two coefficients enables us to determine if feature construction is useful. We can present a system allowing the optimization of preprocessing step : feature selection is applied in all cases; then the two coefficients are calculated for the selected features. With the comparison of the two coefficients, we can decide the importance of feature construction.

In the research of knowledge acquisition based on rough sets theory, attribute reduction is a key problem. Many researchers proposed some algorithms for attribute reduction. Unfortunately, most of them are designed for static data processing. However, many real data are generated dynamically. In this paper, an incremental attribute reduction algorithm is proposed. When new objects are added into a decision information system, a new attribute reduction can be got by this method quickly.