Fuzzy Betweenness Relationship Induces by Fuzzy Partial Order Set

Abstract Many scholars have proposed various methods for constructing fuzzy betweenness relationships, but more scholars tend to induce fuzzy betweenness relationships using crisp partial order relationships. However, there is still a certain gap in research on directly inducing fuzzy betweenness relationships from fuzzy situations. Therefore, this article combines the cut sets and decomposition theorems to connect fuzzy relationships and crisp relationships, assisting in the completion of fuzzy betweenness relationships induced by fuzzy partial order relations. On the completely distributed lattice, the cut sets are defined as four forms of representation, therefore, we provide construction forms for each of the four cut sets corresponding to different situations. These four constructions to some extent fill the gap of fuzzy partial order induced fuzzy betweenness relationships and provide assistance for subsequent research.