Abstract
A fuzzy β covering is a common generalization of partitions, coverings, and fuzzy coverings. Attribute reduction is one of the most popular topics in covering based rough sets. This paper considers the reduction problem for fuzzy β coverings. For the covering reduction, we show that each fuzzy β covering has a unique covering reduct and provide an intuitive algorithm to identify such a reduct. We define the concept of intersection reduction based on fuzzy β neighborhoods and obtain a discernibility matrix-based reduction algorithm to identify all reducts. Finally, as the dual of the intersection reduction, we investigate the union reduction and give its corresponding reduction algorithm.
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