Generating Modular Relaxed Pseudo-metrics by Aggregation

Abstract

[eng] The aggregation of different pieces of information is a well-known practice in the field of applied sciences. Frequently, such information is obtained from metrics and, consequently, the goal is to merge a collection of metrics into a global one. In recent studies, the addition of a parameter to the distance measurement has been essential. Modular metrics completely meet this requirement. Therefore, in this paper we introduce and solve the aggregation problem for a new type of modular metric: the modular relaxed pseudo-metric. This new concept has been introduced to provide a less restrictive distance measurement that does not need to fulfill the axiom of reflexivity, with the aim of covering a wider range of applications. Thus, we characterize the functions that aggregate modular relaxed pseudo-metrics, which we call modular relaxed pseudo-metric aggregation functions. We also compare the results with the modular (pseudo-)metric case. We find that properties such as subadditivity and preservation of triangular triplets are necessary conditions for modular relaxed pseudo-metric aggregation functions, but not sufficient conditions. This shows a difference with modular (pseudo-)metric aggregation functions.