In this paper, we determine when the fuzzy core of a fuzzy binary relation can be obtained in terms of an asymmetric fuzzy binary relation associated with it. We introduce a condition that allows one to obtain semi-convexity for a fuzzy binary relation, one of the main conditions essential in determining a nonempty core.

fuzzy relation, fuzzy, preference, asymmetric, symmetric, complete, reflexive, indifference, conorm, fuzzy core, correspondence, closed-valued, lower section, lower continuous, semi-convex.