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2018 | OriginalPaper | Chapter

Entropy and Monotonicity

Authors : Bernadette Bouchon-Meunier, Christophe Marsala

Published in: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations

Publisher: Springer International Publishing

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Abstract

Measuring the information provided by the observation of events has been a challenge for seventy years, since the simultaneous inception of entropy by Claude Shannon and Norbert Wiener in 1948. Various definitions have been proposed, depending on the context, the point of view and the chosen knowledge representation. We show here that one of the most important common feature in the choice of an entropy is its behavior with regard to the refinement of information and we analyse various definitions of monotonicity.

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previous chapter Consistency Properties for Fuzzy Choice Functions: An Analysis with the Łukasiewicz t-norm
next chapter On the Problem of Comparing Ordered Ordinary Fuzzy Multisets
Footnotes
1
In the following, for the sake of simplicity, \(w_{x_i}\) will be denoted \(w_i\) when the meaning of i is clear.
 
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Metadata
Title
Entropy and Monotonicity
Authors
Bernadette Bouchon-Meunier
Christophe Marsala
Copyright Year
2018
Book
Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations

Print ISBN: 978-3-319-91475-6

Electronic ISBN: 978-3-319-91476-3

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-91476-3_28

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