An Attempt of Object Reduction in Rough Set Theory

Attribute reduction is a popular topic in rough set theory; however, object reduction is not considered popularly. In this paper, from a viewpoint of computing all relative reducts, we introduce a concept of object reduction that reduces the number of objects as long as possible with keeping the results of attribute reduction in the original decision table.INSPEC Accession Number: 1867432

Geometric lattice structure of covering and its application to attribute reduction through matroids

The reduction of covering decision systems is an important problem in data mining, and covering-based rough sets serve as an efficient technique to process the problem. Geometric lattices have been widely used in many fields, especially greedy algorithm design which plays an important role in the reduction problems. Therefore, it is meaningful to combine coverings with geometric lattices to solve the optimization problems. In this paper, we obtain geometric lattices from coverings through matroids and then apply them to the issue of attribute reduction. First, a geometric lattice structure of a covering is constructed through transversal matroids. Then its atoms are studied and used to describe the lattice. Second, considering that all the closed sets of a finite matroid form a geometric lattice, we propose a dependence space through matroids and study the attribute reduction issues of the space, which realizes the application of geometric lattices to attribute reduction. Furthermore, a special type of information system is taken as an example to illustrate the application. In a word, this work points out an interesting view, namely, geometric lattice to study the attribute reduction issues of information systems

Interpretation and reduction of attribute grammars

An attribute grammar (AG) is in reduced form if in all its derivation trees every attribute contributes to the translation. We prove that, eventhough AG are generally not in reduced form, they can be reduced, i.e., put into reduced form, without modifying their translations. This is shown first for noncircular AG and then for arbitrary AG. In both cases the reduction consists of easy (almost syntactic) transformations which do not change the semantic domain of the AG. These easy transformations are formalized by introducing the notion of AG interpretation as an extension to AG of the concept of context-free grammar form. Finally we prove that any general algorithm for reducing even the simple class of L-AG needs exponential time (in the size of the input AG) infinitely often

Knowledge reduction of dynamic covering decision information systems with varying attribute values

Knowledge reduction of dynamic covering information systems involves with the time in practical situations. In this paper, we provide incremental approaches to computing the type-1 and type-2 characteristic matrices of dynamic coverings because of varying attribute values. Then we present incremental algorithms of constructing the second and sixth approximations of sets by using characteristic matrices. We employ experimental results to illustrate that the incremental approaches are effective to calculate approximations of sets in dynamic covering information systems. Finally, we perform knowledge reduction of dynamic covering information systems with the incremental approaches