Next Article in Journal
Lyapunov Functions to Caputo Fractional Neural Networks with Time-Varying Delays
Previous Article in Journal
Yukawa Potential, Panharmonic Measure and Brownian Motion
Article Menu

Export Article

Open AccessArticle
Axioms 2018, 7(2), 29; https://doi.org/10.3390/axioms7020029

A Survey on the Mathematical Foundations of Axiomatic Entropy: Representability and Orderings

1
Institute for Advanced Research in Business and Economics (Inarbe), Departamento de Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain
2
Institute for Advanced Materials (InaMat), Departamento de Física, Universidad Pública de Navarra, 31006 Pamplona, Spain
3
Institute for Advanced Materials (InaMat), Departamento de Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 23 March 2018 / Revised: 16 April 2018 / Accepted: 3 May 2018 / Published: 8 May 2018
Full-Text   |   PDF [440 KB, uploaded 8 May 2018]

Abstract

Different abstract versions of entropy, encountered in science, are interpreted in the light of numerical representations of several ordered structures, as total-preorders, interval-orders and semiorders. Intransitivities, other aspects of entropy as competitive systems, additivity, etc., are also viewed in terms of representability of algebraic structures endowed with some compatible ordering. A particular attention is paid to the problem of the construction of an entropy function or their mathematical equivalents. Multidisciplinary comparisons to other similar frameworks are also discussed, pointing out the mathematical foundations. View Full-Text
Keywords: ordered structures; numerical representations; entropy; representability; utility functions ordered structures; numerical representations; entropy; representability; utility functions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Campión, M.-J.; Gómez-Polo, C.; Induráin, E.; Raventós-Pujol, A. A Survey on the Mathematical Foundations of Axiomatic Entropy: Representability and Orderings. Axioms 2018, 7, 29.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Axioms EISSN 2075-1680 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top