Index spaces and standard indices in metric modelling - ERDOĞAN, EZGİ (My University, 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: Matematik; Bilgisayar Bilimleri; Temel Bilimler; Mühendislik ve Teknoloji; Mathematics; Computer Science; Natural Sciences; Engineering and Technology; MATEMATİK, UYGULAMALI; Temel Bilimler (SCI); MATEMATİK, DİSİPLİNLERARASI UYGULAMALAR; MEKANİK; Mühendislik; Mühendislik, Bilişim ve Teknoloji (ENG); MATHEMATICS, APPLIED; MATHEMATICS; Natural Sciences (SCI); MATHEMATICS, INTERDISCIPLINARY APPLICATIONS; MECHANICS; ENGINEERING; Engineering, Computing & Technology (ENG); Analiz; Uygulamalı matematik; Genel Mühendislik; Cebir ve Sayı Teorisi; Sayısal analiz; Hesaplamalı Matematik; Matematik (çeşitli); Mühendislik (çeşitli); Modelleme ve Simülasyon; Genel Matematik; Hesaplamalı Teori ve Matematik; Fizik Bilimleri; Analysis; Applied Mathematics; General Engineering; Algebra and Number Theory; Numerical Analysis; Computational Mathematics; Mathematics (miscellaneous); Engineering (miscellaneous); Modeling and Simulation; General Mathematics; Computational Theory and Mathematics; Physical Sciences; metric model; index space; standard index; Lipschitz extension; triage