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Approaches to knowledge reduction based on variable precision rough set model. (English) Zbl 1076.68089
Summary: This paper deals with approaches to knowledge reduction based on a variable precision rough set model. The concepts of $\beta$ lower distribution reduct and $\beta$ upper distribution reduct based on Variable Precision Rough Sets (VPRS) are first introduced. Their equivalent definitions are then given, and the relationships among $\beta$ lower and $\beta$ upper distribution reducts and alternative types of knowledge reduction in inconsistent systems are investigated. It is proved that, for some special thresholds, the $\beta$ lower distribution reduct is equivalent to the maximum distribution reduct, whereas the $\beta$ upper distribution reduct is equivalent to the possible reduct. The judgement theorems and discernibility matrices associated with the $\beta$ lower and $\beta$ upper distribution reducts are also established, from which we can obtain the approaches to knowledge reduction in VPRS.
##### MSC:
 68T37 Reasoning under uncertainty