Lattice-valued betweenness relations and its induced lattice-valued convex structures

Article type: Research Article

Authors: Shi, Yi^{a; b} | Shi, Fu-Gui^{a; b; *}

Affiliations: [a] School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China | [b] Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing, P.R. China

Correspondence: [*] Corresponding author. Fu-Gui Shi. Tel.: +86 13488811735; E-mail: fuguishi@bit.edu.cn.

Abstract:  In this paper, we mainly introduce the concept of lattice-valued betweenness relations and study its relationships with L-fuzzifying convex structures in depth. Such an extended betweenness relation is defined to be a map from X × X × X to a complete lattice provided that fulfills a set of axioms. We also discuss the relationships among them and other algebraic and geometric structures. Moreover, a category of approach is provided to present lattice-valued betweenness relations. It is shown that the category of lattice-valued betweenness spaces and the category of lattice-valued geometric interval spaces are isomorphic.

Keywords: Lattice-valued betweenness space, L-fuzzifying convex structure, lattice-valued geometric interval space, L-fuzzifying join space

DOI: 10.3233/JIFS-181395

Journal: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 6, pp. 8523-8533, 2019