On rough and LT-fuzzy sets

A concept of LT-fuzzy sets was introduced by Rasiowa and Cat Ho (1992). LT-fuzzy sets are a modification of L-fuzzy sets introduced by Goguen (1967). We introduce here a notion of a generalized rough set and show that it can be considered as a particular case of a L-fuzzy set. We also generalize the notion of a rough equality of sets, introduced by Pawlak in 1985 to a notion of topological equality of sets and we prove that the LT-fuzzy sets provide a common characterization for all of the considered concepts.