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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 β lower distribution reduct and β upper distribution reduct based on Variable Precision Rough Sets (VPRS) are first introduced. Their equivalent definitions are then given, and the relationships among β lower and β upper distribution reducts and alternative types of knowledge reduction in inconsistent systems are investigated. It is proved that, for some special thresholds, the β lower distribution reduct is equivalent to the maximum distribution reduct, whereas the β upper distribution reduct is equivalent to the possible reduct. The judgement theorems and discernibility matrices associated with the β lower and β upper distribution reducts are also established, from which we can obtain the approaches to knowledge reduction in VPRS.
68T37Reasoning under uncertainty