Open AccessFuzzy points based betweenness relations in L-convex spaces
Author(s) -
Hui Yang,
Bin Pang
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2110521y
Subject(s) - betweenness centrality , mathematics , convex hull , hull , type (biology) , discrete mathematics , regular polygon , combinatorics , pure mathematics , geometry , ecology , marine engineering , centrality , engineering , biology
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.