On the Symmetrization of Quasi-metrics: An Aggregation Perspective

In 1981, Borsik and Dobos studied the problem of how to combine, by means of a function, two metrics in order to obtain a single one as output. To this end, they introduced the notion of metric aggregation function and gave a characterization of such functions ([1]). Recently, in [14], Mayor and Valero have extended the original work of Borsik and Dobos to the context of quasi-metrics in such a way that a general description of how to merge through a function, called quasi-metric aggregation function, two quasi-metrics into a single one has been given. Since every quasi-metric induces, in a natural way, a metric the main purpose of this paper is to mastermind formally the problem of how to symmetrize a quasi-metric and to provide a solution to such a problem based on the main ideas that arise in the quasi-metric aggregation framework. To this end, the notion of metric generating function, those functions that allow to generate a metric from a quasi-metric, is introduced and a full description of such functions is given from an aggregation perspective. Moreover, a relationship between the quasi-metric aggregation problem and the symmetrization one is provided.

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