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Further Considerations of Classification-Oriented and Approximation-Oriented Rough Sets in Generalized Settings
Abstract
Rough sets can be interpreted in two ways: classification of objects and approximation of a set. From this point of view, classification-oriented and approximation-oriented rough sets have been proposed. In this paper, the author reconsiders those two kinds of rough sets with reviewing their definitions, properties and relations. The author describes that rough sets based on positive and negative extensive relations are mathematically equivalent but it is important to consider both because they obtained positive and negative extensive relations are not always in inverse relation in the real world. The difference in size of granules between union-based and intersection-based approximations is emphasized. Moreover, the types of decision rules associated with those rough sets are shown.
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