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arXiv · 2603.10077

Betweenness relations and Fuzzy betweenness relations in fuzzy metric spaces

Yu Zhong
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Abstract

In this paper, we mainly discuss the constructions and the characteristics of betweenness relations and fuzzy betweenness relations in KM-fuzzy metric spaces. And the family of betweenness relations induced by a KM-fuzzy metric form a nest of betweenness relations.The main focus of this paper is to introduce two different construction methods for fuzzy betweenness relations induced by a KM-fuzzy metric.One of them is directly obtained by using the implication operator. The other is through the corresponding nest of metrics of KM-fuzzy metrics. Furthermore, we also show that the two types of fuzzy betweenness relations are the same, and they also satisfy the eight kinds of four-point transitivity properties and the six kinds of five-point transitivity properties.

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Yu Zhong. 2026-03-10. Betweenness relations and Fuzzy betweenness relations in fuzzy metric spaces. https://arxiv.org/abs/2603.10077

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