Index spaces and standard indices in metric modelling - Erdoğan, Ezgi; Ferrer-Sapena, Antonia; Jiménez-Fernández, Eduardo; Sánchez-Pérez, Enrique A. (Nonlinear Analysis: Modelling and Control, 2022)
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.
Keywords: metric model; index space; standard index; Lipschitz extension; triage