The $L$-fuzzy approximation operator associated with an $L$-fuzzy approximation space $(X,R)$ turns out to be a saturated $L$-fuzzy closure (interior) operator on a set $X$ precisely when the relation $R$ is reflexive and transitive. We investigate the relations between $L$-fuzzy approximation spaces and $L$-(fuzzy) topological spaces.

Given a finite set D of positive integers, the distance graph G(Z,D) has Z as the vertex set and {ij : |i−j| ∈ D} as the edge set. Given D, the asymptotic clique covering ratio is defined as S(D) = lim sup n→∞ n cl(n) , where cl(n) is the minimum number of cliques covering any consecutive n vertices of G(Z,D). The parameter S(D) is closely related to the ratio spT(G) χ(G) of a graph G, where χ(...