Fuzzy points based betweenness relations in L-convex spaces

Abstract

As topology-like mathematical structures, convex structures can be 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.