Related family: A new method for attribute reduction of covering information systems

In terms of attribute reduction of covering based rough sets, the discernibility matrix is used as a conventional method to compute all attribute reducts. However, it is inapplicable to attribute reduction in certain circumstances. In this article, a new method, referred to as the related family, is introduced to compute all attribute reducts and relative attribute reducts for covering rough sets. Its core idea is to remove superfluous attributes while keeping the approximation space of covering information system unchanged. The related family method is more powerful than the discernibility matrix method, since the former can handle complicated cases that could not be handled by the latter. In addition, a simplified version of the related family and its corresponding heuristic algorithm are also presented.