The unified extropy and its versions in classical and Dempster–Shafer theories
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 introdu...
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| Published in | Journal of applied probability Vol. 61; no. 2; pp. 685 - 696 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Cambridge, UK
Cambridge University Press
01.06.2024
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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. |
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| AbstractList | 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. |
| Author | Longobardi, Maria Buono, Francesco Deng, Yong |
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| Cites_doi | 10.1109/ACCESS.2019.2939332 10.3390/e22050582 10.1016/j.chaos.2016.07.014 10.1214/aoms/1177698950 10.1239/jap/1025131441 10.1007/s11432-020-3006-9 10.1109/TIT.2004.828057 10.1016/j.physa.2022.127214 10.3390/e23050623 10.1016/j.physleta.2009.05.026 10.1109/IFIC.2000.862713 10.1016/j.spl.2021.109241 10.1515/9780691214696 10.1017/jpr.2017.6 10.1214/14-STS430 10.1080/03610926.2021.1980049 10.1002/j.1538-7305.1948.tb01338.x 10.1007/BF01016429 |
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| Copyright | The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust |
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| DOI | 10.1017/jpr.2023.68 |
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| Keywords | extropy Tsallis entropy 62B10 94A17 Shannon entropy fractional entropy 62H30 Dempster–Shafer theory |
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| Title | The unified extropy and its versions in classical and Dempster–Shafer theories |
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