Index spaces and standard indices in metric modelling
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Metric modelIndex spaceStandard indexLipschitz extensionTriage
Erdoğan E... [et al.] (2022). Index spaces and standard indices in metric modelling. Nonlinear Analysis: Modelling and Control, 27, 1-20. [https://doi.org/10.15388/namc.2022.27.27493]
SponsorshipMCIN/AEI PID2019-105708RB; ERDF A way of making Europe; Catedra de Transparencia y Gestion de Datos, Universitat Politecnica de Valencia, Generalitat Valenciana
We analyze the basic structure of certain metric models, which are constituted by an index I acting on a metric space (D; d) representing a relevant property of the elements of D. We call such a structure (D; d; I) an index space and define on it normalization and consistency constants that measure to what extent I is compatible with the metric d. The “best” indices are those with such constants equal to 1 (standard indices), and we show an approximation method for other indices using them. With the help of Lipschitz extensions, we show how to apply these tools: a new model for the triage process in the emergency department of a hospital is presented.