Index spaces and standard indices in metric modelling

IF 2.6 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Modelling and Control Pub Date : 2022-05-10 DOI:10.15388/namc.2022.27.27493

E. Erdoğan, A. Ferrer-Sapena, E. Jiménez-Fernández

引用次数: 0

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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度量建模中的索引空间和标准索引

我们分析了某些度量模型的基本结构，这些度量模型由作用在度量空间（D；D）上的索引I构成，该度量空间表示D的元素的相关性质。我们将这种结构（D；D；I）称为索引空间，并在其上定义规范化和一致性常数，这些常数衡量I与度量D的兼容程度。“最佳”指数是那些常数等于1的指数（标准指数），我们展示了使用它们的其他指数的近似方法。在Lipschitz扩展的帮助下，我们展示了如何应用这些工具：为医院急诊科的分诊过程提供了一个新的模型。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Nonlinear Analysis-Modelling and Control MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.80

自引率

10.00%

发文量

审稿时长

9.6 months

期刊介绍： The scope of the journal is to provide a multidisciplinary forum for scientists, researchers and engineers involved in research and design of nonlinear processes and phenomena, including the nonlinear modelling of phenomena of the nature. The journal accepts contributions on nonlinear phenomena and processes in any field of science and technology. The aims of the journal are: to provide a presentation of theoretical results and applications; to cover research results of multidisciplinary interest; to provide fast publishing of quality papers by extensive work of editors and referees; to provide an early access to the information by presenting the complete papers on Internet.