A new approach to the fuzzification of arity, JHC and CUP of L-convexities

Fuzzy structures induced by fuzzy betweenness relations

“…In recent years, the study of fuzzy convex structures has witnessed an increasing interest, and this from points of view, such as topology [27,48,50,57], convergence theory [32,49,56], category theory [21,22,30], interval theory [28,31,47], geometry [9,44,45,46], and so on. From the perspective of fuzzy order relations, Li and Shi [24] studied some properties of L-fuzzifying convex structures induced by L-orders, where L is a completely distributive lattice.…”

On the disjoint sums of M-fuzzifying convex spaces

“…Notation. According to the above definition, it is evident that ary(C ) ≤ n iff it satisfies the equality (2), this happens to be the definition of arity ≤ n given in [26].…”

“…Subsequently, Maruyama [13] further proposed the notion of L-fuzzy convex spaces under the framework of a completely distributive lattice L. In both cases of fuzzy convex spaces and L-fuzzy convex spaces, every convex set is fuzzy, but the convex space formed by these fuzzy convex sets is thought to be crisp. Recently, L-convex structures are studied by many researchers in [2,7,9,15,16,18,29].…”