On aggregation of metric structures: the extended quasi-metric case

Abstract

In 1981, J. Borsík and J. Doboš studied and solved the problem of how to merge, by means of a function, a (not necessarily finite) collection of metrics in order to obtain a single one as output. Later on, in 2010, G. Mayor and O. Valero proposed and solved the Borsík and Doboš problem in the context of quasi-metrics. In this paper, we focus our attention on the aggregation problem for the case of extended quasi-metrics and we give several connections between both problems, the problem of merging quasi-metrics and the extended quasi-metric aggregation one.

Keywords:

• Aggregation
• (extended) quasi-metric
• monotone function
• subadditive function