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基于总不确定性度量的信念函数否定

Negation of Belief Function Based on the Total Uncertainty Measure.

作者信息

Xie Kangyang, Xiao Fuyuan

机构信息

School of Computer and Information Science, Southwest University, No. 2 Tiansheng Road, BeiBei District, Chongqing 400715, China.

出版信息

Entropy (Basel). 2019 Jan 15;21(1):73. doi: 10.3390/e21010073.

DOI:10.3390/e21010073
PMID:33266789
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7514182/
Abstract

The negation of probability provides a new way of looking at information representation. However, the negation of basic probability assignment (BPA) is still an open issue. To address this issue, a novel negation method of basic probability assignment based on total uncertainty measure is proposed in this paper. The uncertainty of non-singleton elements in the power set is taken into account. Compared with the negation method of a probability distribution, the proposed negation method of BPA differs becausethe BPA of a certain element is reassigned to the other elements in the power set where the weight of reassignment is proportional to the cardinality of intersection of the element and each remaining element in the power set. Notably, the proposed negation method of BPA reduces to the negation of probability distribution as BPA reduces to classical probability. Furthermore, it is proved mathematically that our proposed negation method of BPA is indeed based on the maximum uncertainty.

摘要

概率的否定提供了一种看待信息表示的新方法。然而，基本概率赋值（BPA）的否定仍是一个未解决的问题。为解决此问题，本文提出了一种基于总不确定性度量的基本概率赋值的新型否定方法。考虑了幂集中非单元素的不确定性。与概率分布的否定方法相比，所提出的BPA否定方法有所不同，因为某个元素的BPA被重新分配到幂集中的其他元素，重新分配的权重与该元素和幂集中每个其余元素的交集基数成比例。值得注意的是，当BPA简化为经典概率时，所提出的BPA否定方法简化为概率分布的否定。此外，数学证明了我们提出的BPA否定方法确实基于最大不确定性。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1463/7514182/16c86e85d2a3/entropy-21-00073-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1463/7514182/6d249142b3ec/entropy-21-00073-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1463/7514182/a89bc90fdc8b/entropy-21-00073-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1463/7514182/9d73e6e4ca45/entropy-21-00073-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1463/7514182/1b3895c8bac2/entropy-21-00073-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1463/7514182/16c86e85d2a3/entropy-21-00073-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1463/7514182/6d249142b3ec/entropy-21-00073-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1463/7514182/a89bc90fdc8b/entropy-21-00073-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1463/7514182/9d73e6e4ca45/entropy-21-00073-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1463/7514182/1b3895c8bac2/entropy-21-00073-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1463/7514182/16c86e85d2a3/entropy-21-00073-g005.jpg

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Entropy (Basel). 2018 Nov 3;20(11):842. doi: 10.3390/e20110842.
3
Analysis of Heat Dissipation and Reliability in Information Erasure: A Gaussian Mixture Approach.
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Entropy (Basel). 2020 Feb 7;22(2):195. doi: 10.3390/e22020195.
信息擦除中的散热与可靠性分析：一种高斯混合方法。
Entropy (Basel). 2018 Sep 30;20(10):749. doi: 10.3390/e20100749.
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Chaos. 2018 Apr;28(4):043109. doi: 10.1063/1.5030894.
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