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A novel belief Tanimoto coefficient with its applications in multisource information fusion

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Yuhang Lu
Yuhang Lu
Yuhang Lu
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Fuyuan Xiao
Fuyuan Xiao
Fuyuan Xiao
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Abstract and Figures

Dempster-Shafer evidence theory (DST) is a versatile framework for handling uncertainty and provides a reliable method for data fusion. Managing conflicts between multiple bodies of evidence (BOEs) within DST poses a challenging problem that necessitates effective strategies. In this paper, we present a novel similarity measurement called the belief Tanimoto coefficient (BTC). The BTC accurately quantifies the consistency between BOEs by considering both the length and direction of the evidence vectors. Furthermore, we propose a conflict measurement approach based on BTC. We analyze and demonstrate the desirable properties of the proposed similarity and conflict measures. Numerical examples and comparisons are provided to illustrate the superior effectiveness and validity of BTC. Additionally, we introduce a multisource information fusion method called BTC-MSIF. The proposed BTC-MSIF method achieves higher accuracy rates compared to existing approaches in real-world scenarios, including fault diagnosis and pattern classification.
The constraint of α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \alpha $$\end{document} and β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \beta $$\end{document} in Example 1
The constraint of α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \alpha $$\end{document} and β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \beta $$\end{document} in Example 1
… 
The similarity BTC(m1,m2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \textrm{BTC}(m_1,m_2)$$\end{document} varies with α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} and β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \beta $$\end{document}
The similarity BTC(m1,m2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \textrm{BTC}(m_1,m_2)$$\end{document} varies with α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} and β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \beta $$\end{document}
… 
The belief Tanimoto conflict kBTC(m1,m2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ k_\textrm{BTC}(m_1,m_2)$$\end{document} varies with α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} and β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \beta $$\end{document}
The belief Tanimoto conflict kBTC(m1,m2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ k_\textrm{BTC}(m_1,m_2)$$\end{document} varies with α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} and β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \beta $$\end{document}
… 
The conflict trends under different approaches in Example 8
The conflict trends under different approaches in Example 8
… 
The flowchart of experiment process
+2
The flowchart of experiment process
… 
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Applied Intelligence (2024) 54:985–1002
https://doi.org/10.1007/s10489-023-05217-9
A novel belief Tanimoto coefficient with its applications in multisource
information fusion
Yuhang Lu1·Fuyuan Xiao1
Accepted: 6 December 2023 / Published online: 28 December 2023
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023
Abstract
Dempster-Shafer evidence theory (DST) is a versatile framework for handling uncertainty and provides a reliable method for
data fusion. Managing conflicts between multiple bodies of evidence (BOEs) within DST poses a challenging problem that
necessitates effective strategies. In this paper, we present a novel similarity measurement called the belief Tanimoto coefficient
(BTC). The BTC accurately quantifies the consistency between BOEs by considering both the length and direction of the
evidence vectors. Furthermore, we propose a conflict measurement approach based on BTC. We analyze and demonstrate the
desirable properties of the proposed similarity and conflict measures. Numerical examples and comparisons are provided to
illustrate the superior effectiveness and validity of BTC. Additionally, we introduce a multisource information fusion method
called BTC-MSIF. The proposed BTC-MSIF method achieves higher accuracy rates compared to existing approaches in
real-world scenarios, including fault diagnosis and pattern classification.
Keywords Dempster-Shafer evidence theory ·Conflict management ·Belief Tanimoto coefficient ·Multisource information
fusion ·Decision-making ·Fault diagnosis ·Pattern classification
1 Introduction
Due to the complexity of the real world and the uncertainty
of objectives, a single source of data cannot fully and accu-
rately depict all relevant information about the target [1].
Therefore, multisource information fusion (MSIF) becomes
essential to fill in the gaps and provide a comprehensive and
reliable understanding of the situation [2]. MSIF is a pow-
erful and intricate assessment process that combines data
from diverse and potentially conflicting sources to enable
users to evaluate complex scenarios and make precise deci-
sions. Recently, how to obtain high-reliability fusion results
in MSIF has attracted much attention [3]. Quantifying uncer-
tainty is a crucial part of multisource information fusion
[4]. There are considerable theories have been proposed to
deal with the uncertainty, including extended fuzzy sets [5],
rough sets [6], evidence theory [7] and other hybrid methods
BFuyuan Xiao
doctorxiaofy@hotmail.com; xiaofuyuan@cqu.edu.cn
Yuhang Lu
luyuhangcqu@163.com
1School of Big Data and Software Engineering, Chongqing
University, 401331 Chongqing, China
[8,9]. These theories are broadly applied in many fields
ranging from medicine to engineering [10], such as medical
diagnosis [11], open set recognition [12], fault analysis [13],
dynamics modeling of multi-agent learning [14,15], rapid
source localization [16], image scene classification [17] and
decision making [18,19].
Among these theories, DST is an effective tool to manage
the uncertainty [20,21], which satisfies the associative law
and commutative law, generalizes the uncertainty to subsets
by basic probability assignment (BPA). Furthermore, DST is
easily implemented and can be applied in real applications
conveniently, such as risk evaluation [22], classification [23],
time series analysis [24,25], uncertain database retrieval
[26], etc.
Therefore, DST plays a significant role in uncertainty
measure and decision making, which has been broadly inves-
tigated and developed, such as probability transformation
[27,28], evidence reasoning [29,30], belief rule base [31,
32], random permutation set [33–36], quantum evidence the-
ory [37–39] etc. In the classical DST framework, many
scholars have explored the issue of conflict management
among BOEs from various perspectives such as distance [40],
correlation coefficients [41], and divergence [42]. Research
[43] has demonstrated that effective conflict management
123
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... The second category involves using different credibility distances to measure the similarity between pieces of evidence, followed by a fusion process based on similarity [55][56][57]. Evidence distance is used to measure and compare the differences and consistencies between different sources of evidence, where smaller distances indicate greater consistency between the evidence, and larger distances indicate greater inconsistency. ...
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