Aggregating distances with uncertainty: the modular (pseudo-)metric case

Abstract

[eng] Many real problems involve the use of metrics to be solved. In such problems to merge some measurements obtained through the used metric is often needed in order to make a working decision. So functions that merge a collection of metrics providing a new one as output have roused interest of different authors. Nevertheless, the axiomatic that defines the concept of metric limits their applicability in some situations. Motivated by this fact, different generalizations of the concept of metric can be found in the literature. Among them, it is worth mentioning the notion of modular metric introduced by Chistyakov. This kind of metric involves uncertainty due to the inclusion of a parameter in the distance evaluation. The aim of this paper consists in characterizing those functions that merge a collection of modular (pseudo-)metrics into a new modular (pseudo-)metric, all of them defined on the same set.