Generalizations of Rough Sets: From Crisp to Fuzzy Cases

Rough sets can be interpreted in two ways: classification of objects and approximation of a set. In this paper, we discuss the differences and similarities of generalized rough sets based on those two different interpretations. We describe the relations between generalized rough sets and types of extracted decision rules. Moreover, we extend the discussion to fuzzy rough sets. Through this paper, the relations among generalized crisp rough sets and fuzzy rough sets are clarified and two different directions of applications in rule extraction are suggested.