In this paper, we present two approaches to define convex fuzzy cone. First, by the use of the relations between fuzzy points and fuzzy subsets, definitions of (,)-convex fuzzy cones are given. We have shown that the acceptable non-trivial concepts obtained in this manner are the (∈,∈)-convex fuzzy cone, (∈,∈∨q)-convex fuzzy cone and (∈,∈,∨-convex fuzzy cone. Second, based on the theory of a consensus space presented by Hisakichi Suzuki, concept of C-convex fuzzy cone is acquired. It is pointed that (∈,∈)-...