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The main objective of the paper is to introduce a new algorrithm of attribute reducts based on variable precision rough set theory. An improved genetic algorithm (GA) which adopts information entropy as it’s fitness function is introduced. The strategy of mixed crossover and two points mutation enlarges the search scope. The cross generation elicit selection and self-adapting strategy make the genetic algorithm converge to the overall optimal solution stably and quickly, which gives it an edge over the normal GA. The effectiveness and the advantage with respect to the norm GA are checked though an example.

The reduction theory is the most significant component of rough set theory. This paper for the first time employs the topological separability to analyze the reductions of covering rough sets. First, a definition is given to the covering separability to describe the classification ability of knowledge bases. Second, a connection is built between the separability and discernibility matrix. The knowledge bases which do not satisfy the separability are transformed to ones with separability via the application of the topological method, and then discernibility matrices with lower orders are reached. As a significant advantage, the method simplifies discernibility matrices to lower order, and in turn improves all reduction algorithm based on discernibility matrix.