Fuzzy betweenness relations and their connection with fuzzy order relations

Abstract

Fuzzy relations and, in particular, fuzzy order relations, have been largely studied since Zadeh first introduced the concept back in 1971. Bearing in mind that betweenness relations and their relationship with order relations have historically attracted the attention of mathematicians, it is very surprising that the study of fuzzy betweenness relations has had a very limited scientific reach so far, and barely no attention has been given to their relationship with fuzzy order relations. In this manuscript, we study fuzzy betweenness relations in depth and discuss their connection with both schools of thought in the study of fuzzy order relations: the already mentioned one introduced by Zadeh and the one initiated by Höhle and Blanchard and popularized by Bodenhofer.