*-betweenness induced by fuzzy metrics

Motivated by Zhang et al. [28,38,39], we aim to make a further discussion of *-betweenness relations. In this paper, we provide the method to construct the *-betweenness by GV fuzzy metrics. After considering the description of *-equivalence with respect to strong fuzzy metrics, we investigate the construction of *-E-betweenness. Some properties of *-betweenness and *-Ebetweenness are discussed and some conclusions or conditions in [28] are verified. This paper is also a supplement of [28]. Finally, the relationship between fuzzifying convex structures and *-betweenness relations has been studied.