In this paper the concept of fuzzy contra -continuity in the sense of A. P. Sostak (1985) is introduced. Some interesting properties and characterizations are investigated. Also, some applications to fuzzy compact spaces are established.
The resemblance relation is used to reflect some real life situations for which a fuzzy equivalence is not suitable. We study the properties of cuts for such relations. In the case of a resemblance on a real line we show that it determines a special family of crisp functions closely connected to its cut relations. Conversely, we present conditions which should be satisfied by a collection of real functions in in order that this collection determines a resemblance relation.