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The unified extropy and its versions in classical and Dempster–Shafer theories

Part of: Communication, information Sufficiency and information Multivariate analysis

Published online by Cambridge University Press:  23 October 2023

Francesco Buono Open the ORCID record for Francesco Buono [Opens in a new window] ,
Yong Deng  and
Maria Longobardi Open the ORCID record for Maria Longobardi [Opens in a new window]
Francesco Buono*
Affiliation:
Università di Napoli Federico II
Yong Deng*
Affiliation:
University of Electronic Science and Technology of China
Maria Longobardi*
Affiliation:
Università di Napoli Federico II
*
*Postal address: Università di Napoli Federico II, Naples, Italy.
**Postal address: RWTH Aachen University, Aachen, Germany. Email address: francesco.buono3@unina.it
***Postal address: University of Electronic Science and Technology of China, China. Email address: dengentropy@uestc.edu.cn
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Abstract

Measures of uncertainty are a topic of considerable and growing interest. Recently, the introduction of extropy as a measure of uncertainty, dual to Shannon entropy, has opened up interest in new aspects of the subject. Since there are many versions of entropy, a unified formulation has been introduced to work with all of them in an easy way. Here we consider the possibility of defining a unified formulation for extropy by introducing a measure depending on two parameters. For particular choices of parameters, this measure provides the well-known formulations of extropy. Moreover, the unified formulation of extropy is also analyzed in the context of the Dempster–Shafer theory of evidence, and an application to classification problems is given.

Keywords

Shannon entropyextropyDempster–Shafer theoryTsallis entropyfractional entropy

MSC classification

Primary: 62B10: Information-theoretic topics
Secondary: 62H30: Classification and discrimination; cluster analysis 94A17: Measures of information, entropy
Type
Original Article
Information
Journal of Applied Probability , Volume 61 , Issue 2 , June 2024 , pp. 685 - 696
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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