Fuzzy Points Based Betweenness Relations in L-Convex Spaces

As topology-like mathematical structures, convex structures can be characterized by betweenness relations via (restricted) hull operators in convex spaces. In a topological approach, the aim of this paper is to present the fuzzy counterpart of betweenness relations based on fuzzy points in fuzzy convex spaces. Concretely, the notion of L-betweenness relations via restricted L-hull operators is introduced. Firstly, it is proved that L-betweenness relations are categorically isomorphic to restricted L-hull operators and L-remotehood systems, respectively. Secondly, it is shown that L-betweenness relations from two perspectives of restricted L-hull operators and L-remotehood systems are unified. Finally, a new type of restricted L-hull operators in accordance with L-betweenness relations is proposed and the relationship between two types of restricted L-hull operators is displayed.