Abstract
Rough sets have been widely studied and applied in every field. There are various theories related or aligned with rough- set theories. In this article, we study the properties of well-behaved classifiers, in which all the characterized upper bounds and lower bounds are based and closed under set operations, including union, intersection and complement. We show every equivalence-relation-induced classifier indeed is a well-behaved classifier. We also show the necessary and suf- ficient conditions for being a well-behaved classifier. In addition to that, an algorithm to decide whether a given classier is a well-behaved one or not is also derived in this article.
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