Fuzzy rough sets: beyond the obvious

Martine De Cock, Chris Cornelis, Etienne E. Kerre

Abstract: Rough set theory was introduced in 1982. Soon it was combined with fuzzy set theory, giving rise to a hybrid model, involving fuzzy sets and fuzzy relations, which appears to be a natural, elegant generalization. In this paper we reveal that in the fuzzification process an important step seems to be overlooked. The most fascinating part is that this forgotten step arises from the true essence of fuzzy set theory: namely, that an element can belong to a given degree to more than one fuzzy set at the same time.