Index spaces and standard indices in metric modelling
Articles
Ezgi Erdoğan
Marmara University
https://orcid.org/0000-0002-0641-1930
Antonia Ferrer-Sapena
Universitat Politècnica de València
https://orcid.org/0000-0001-6432-917X
Eduardo Jiménez-Fernández
Universidad de Granada
https://orcid.org/0000-0001-6108-527X
Published 2022-05-10
https://doi.org/10.15388/namc.2022.27.27493
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Keywords

metric model
index space
standard index
Lipschitz extension
triage

How to Cite

Erdoğan E., Ferrer-Sapena A. and Jiménez-Fernández E. (2022) “Index spaces and standard indices in metric modelling”, Nonlinear Analysis: Modelling and Control, 27(4), pp. 803-822. doi: 10.15388/namc.2022.27.27493.

Abstract

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.

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