In this paper the concept of fuzzy contra ${}_{\delta }$-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.

In this paper, two kinds of remote neighborhood operators in $(L,M)$-fuzzy convex spaces are proposed, which are called convex $(L,M)$-fuzzy remote neighborhood operators. It is proved that these two kinds of convex $(L,M)$-fuzzy remote neighborhood operators can be used to characterize $(L,M)$-fuzzy convex structures. In addition, the lattice structures of two kinds of convex $(L,M)$-fuzzy remote neighborhood operators are also given.

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 $E$ 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 $E$ in order that this collection determines a resemblance relation.