Many-valued preorders II: The symmetry axiom and probabilistic geometry

Abstract

This paper is a continuation of Part I (Höhle, Many-valued preorders I: the basis of many-valued mathematics (in this volume) [10]) and explains the symmetrization of many-valued preorders and the subsequent quotient construction. An application of these concepts to probabilistic geometry leads to [0, 1]-valued metric spaces which appear as quotient of Menger spaces.