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Multifractal analysis of mass function

In order to explore the fractal characteristic in Dempster–Shafer evidence theory, a fractal dimension of mass function is proposed recently, to reveal the invariance of scale of belief entropy. When mass function degenerates to probability, the fractal dimension is equivalent to classical Renyi inf...

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Autores principales: Qiang, Chenhui, Li, Zhen, Deng, Yong
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10233544/
https://www.ncbi.nlm.nih.gov/pubmed/37362275
http://dx.doi.org/10.1007/s00500-023-08502-4
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author Qiang, Chenhui
Li, Zhen
Deng, Yong
author_facet Qiang, Chenhui
Li, Zhen
Deng, Yong
author_sort Qiang, Chenhui
collection PubMed
description In order to explore the fractal characteristic in Dempster–Shafer evidence theory, a fractal dimension of mass function is proposed recently, to reveal the invariance of scale of belief entropy. When mass function degenerates to probability, the fractal dimension is equivalent to classical Renyi information dimension only with [Formula: see text] , which can measure the change rate of Shannon entropy with the size of framework. For Renyi dimension, different parameters [Formula: see text] represent the relationship between different entropies and framework size. However, this compatibility is not shown in existing fractal dimension. Thus, in this paper, we introduce parameter [Formula: see text] to generalize the existing dimension. Due to the diversity of the value of [Formula: see text] , we name the new dimension: multifractal dimension of mass function. In addition, inspired by multifractal spectrum of Cantor set, we explore the relation between the belief degree of focal element and the number of focal element with same belief degree for some special assignments. Relevant results are also presented by spectrum. We provide a static discounting coefficient generating method to modify mass function to improve the accuracy of classify result. The experiment is conducted in three datasets, and the result shows the effectiveness of our method.
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spelling pubmed-102335442023-06-01 Multifractal analysis of mass function Qiang, Chenhui Li, Zhen Deng, Yong Soft comput Mathematical Methods in Data Science In order to explore the fractal characteristic in Dempster–Shafer evidence theory, a fractal dimension of mass function is proposed recently, to reveal the invariance of scale of belief entropy. When mass function degenerates to probability, the fractal dimension is equivalent to classical Renyi information dimension only with [Formula: see text] , which can measure the change rate of Shannon entropy with the size of framework. For Renyi dimension, different parameters [Formula: see text] represent the relationship between different entropies and framework size. However, this compatibility is not shown in existing fractal dimension. Thus, in this paper, we introduce parameter [Formula: see text] to generalize the existing dimension. Due to the diversity of the value of [Formula: see text] , we name the new dimension: multifractal dimension of mass function. In addition, inspired by multifractal spectrum of Cantor set, we explore the relation between the belief degree of focal element and the number of focal element with same belief degree for some special assignments. Relevant results are also presented by spectrum. We provide a static discounting coefficient generating method to modify mass function to improve the accuracy of classify result. The experiment is conducted in three datasets, and the result shows the effectiveness of our method. Springer Berlin Heidelberg 2023-06-01 /pmc/articles/PMC10233544/ /pubmed/37362275 http://dx.doi.org/10.1007/s00500-023-08502-4 Text en © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Mathematical Methods in Data Science
Qiang, Chenhui
Li, Zhen
Deng, Yong
Multifractal analysis of mass function
title Multifractal analysis of mass function
title_full Multifractal analysis of mass function
title_fullStr Multifractal analysis of mass function
title_full_unstemmed Multifractal analysis of mass function
title_short Multifractal analysis of mass function
title_sort multifractal analysis of mass function
topic Mathematical Methods in Data Science
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10233544/
https://www.ncbi.nlm.nih.gov/pubmed/37362275
http://dx.doi.org/10.1007/s00500-023-08502-4
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