Modular Quasi-pseudo Metrics and the Aggregation Problem

Maria del Mar Bibiloni-Femenias; Oscar Valero

doi:10.20944/preprints202405.1133.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 16 May 2024 / Approved: 16 May 2024 / Online: 17 May 2024 (17:22:10 CEST)

The applicability of the distance aggregation problem has attracted the interest of many authors. Motivated by this fact, in this paper we face the modular quasi-(pseudo-)metric aggregation problem. We characterize those functions that allow merging a collection of modular quasi-(pseudo-)metrics into a single one. Specifically, a description of such functions in terms of triangle triplets is given and, in addition, the relationship between modular quasi-(pseudo-)metric aggregation functions and modular (pseudo-)metric aggregation functions is discussed. Such characterizations are illustrated with appropriate examples. A few methods to construct modular quasi-(pseudo-)metrics are yielded. Several properties of modular quasi-(pseudo-)metric aggregation functions are explored and used to develop quick tests for discarding candidate functions to aggregate modular quasi-(pseudo-)metrics. Moreover, a characterization of those modular quasi-(pseudo-)metric aggregation functions that preserve modular quasi-(pseudo-)metrics is also provided. Furthermore, the relationship between modular quasi-(pseudo-)metric aggregation functions and quasi-(pseudo-)metric aggregation functions is studied in such a way that significative differences are displayed.

modular quasi-pseudo metric; quasi-pseudo metric; aggregation; monotony; subadditivity; triangle triplet

Computer Science and Mathematics, Geometry and Topology

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Modular Quasi-pseudo Metrics and the Aggregation Problem

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