Characterizing quasi-metric aggregation functions

In this paper, we study those functions that allows us to combine a family of quasi-metrics, defined all of them on the same set, into a single one, which will be called quasi-metric aggregation functions. In particular, we characterize the quasi-metric aggregation functions and, in addition, we discuss a few of their properties. Moreover, a few methods to discard those functions that are useless as quasi-metric aggregation functions are introduced. Throughout the paper, different examples justify and illustrate the results presented. Finally, two possible fields where the developed theory can be useful are exposed.