The induction of classification rules has been dominated by a single generic technique—the covering algorithm. This approach employs a simple hill-climbing search to learn sets of rules. Such search is subject to numerous widely known deficiencies. Further, there is a growing body of evidence that learning redundant sets of rules can improve predictive accuracy. The ultimate end-point of a move...

1. A few years ago Rogers [1] showed that, if K is any convex body in n-dimensional Euclidian space, there is a covering of the whole space by translates of K with density less than nlogn+nloglogn+5n, provided n > 3. However the fact that the covering density is reasonably small does not imply that the maximum multiplicity is also small. In the natural covering of space by closed cubes, the den...

Rough set theory provides a systematic way for rule extraction, attribute reduction and knowledge classification in information systems. Some measurements are important in rough sets. For example, information entropy, knowledge dependency are useful in attribute reduction algorithms. This paper proposes the concepts of the lower and upper covering numbers to establish measurements in covering-b...

spherical and hyperbolic space. It is divided into two equal-sized parts: the first is devoted to the two-dimensional case, where much more is known than in the n-dimensional setting, which is discussed in the second part. In addition, there is an appendix providing some important background information, essentially from convex geometry. Many of the sections end with interesting and stimulating...