Article
Version 1
Preserved in Portico This version is not peer-reviewed
Modular Quasi-pseudo Metrics and the Aggregation Problem
Version 1
: Received: 16 May 2024 / Approved: 16 May 2024 / Online: 17 May 2024 (17:22:10 CEST)
How to cite: Bibiloni-Femenias, M. D. M.; Valero, O. Modular Quasi-pseudo Metrics and the Aggregation Problem. Preprints 2024, 2024051133. https://doi.org/10.20944/preprints202405.1133.v1 Bibiloni-Femenias, M. D. M.; Valero, O. Modular Quasi-pseudo Metrics and the Aggregation Problem. Preprints 2024, 2024051133. https://doi.org/10.20944/preprints202405.1133.v1
Abstract
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.
Keywords
modular quasi-pseudo metric; quasi-pseudo metric; aggregation; monotony; subadditivity; triangle triplet
Subject
Computer Science and Mathematics, Geometry and Topology
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment
