基于信任度和确定度的证据加权组合方法

doi:10.11959/j.issn.1000-436x.2017010

摘要/Abstract

摘要：

针对高冲突条件下 Dempster 规则失效的问题，提出一种基于信任度和确定度的证据加权组合方法。首先，对传统证据冲突度量方法—夹角余弦进行了修正，使其能有效处理证据中包含非单子集焦元的情况，并基于其建立了证据信任度模型；其次，为综合反映证据体包含非单子集焦元的程度以及证据体概率分配函数的离散程度，建立了基于证据精度与证据熵的证据确定度模型；然后将信任度与确定度结合来确定证据权重；最后依此权重对证据进行加权平均，并使用 Dempster 规则对平均后的证据进行组合。算例分析表明，与传统证据加权组合方法相比，所提方法在冲突消减和聚焦能力2个方面都具有更好的性能。

关键词: 证据组合, 信任度, 确定度, 冲突度量, 精度, 熵

Abstract:

To overcome the invalidation problem of Dempster rule with high conflict,a weighted combination method based on degree of credibility and certainty was proposed.Firstly,the cosine similarity was modified to hold the ability to measure the evidence conflict when multi-subset focal elements were included,followed by the building of evidence credibility model.Secondly,the evidence certainty model based on precision and entropy was presented,which can both reflect the evidence’s degree of multi-subset focal elements and the dispersion degree of probability assignment.Then the weighted coefficient was determined by credibility and certainty.Finally,the normalized weighted coefficient was used to average the basic probability assignment,and the final combination result can be obtained according to Dempster rule.Numerical examples show that,compared with other traditional weighted combination methods,the proposed approach has made better performance in reducing conflict and accelerating convergence.

Key words: combination of evidences, credibility degree, certainty degree, conflict measurement, precision, entropy

中图分类号:

TP391

王路,邢清华,毛艺帆. 基于信任度和确定度的证据加权组合方法[J]. 通信学报, 2017, 38(1): 83-88.

Lu WANG,Qing-hua XING,Yi-fan MAO. Weighted evidence combination based on degree of credibility and certainty[J]. Journal on Communications, 2017, 38(1): 83-88.

图/表 3

表1

不同情形下的BPA"

情形	BPA
情形1	m₁(θ₁)=m₁(θ₂)=0.5
情形1	m₂(θ₁)=m₂(θ₂)=0.5
情形2	m₁(θ₁)=m₁(θ₂)=0.5
情形2	m₂(θ₃)=m₂(θ₄)=0.5
情形3	$m_{1} (θ_{1}) = m_{1} (θ_{2}) = m_{1} (θ_{3}) = \frac{1}{3}$
情形3	$m_{2} (θ_{4}) = m_{2} (θ_{5}) = m_{2} (θ_{6}) = \frac{1}{3}$
情形4	m(θ₁)=1
情形4	m₂(θ₁θ₂)=m₂(θ₁θ₃)=0.5

表1

图1

表2

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方法	m₁,m₂	m₁,m₂,m₃	m₁,m₂,m₃,m₄	m₁,m₂,m₃,m₄,m₅
	m(θ₁)=0	m(θ₁)=0	m(θ₁)=0	m(θ₁)=0
Dempster	m(θ₂)=0.857 1	m(θ₂)=0.631 6	m(θ₂)=0.328 8	m(θ₂)=0.140 4
	m(θ₃)=0.142 9	m(θ₃)=0.368 4	m(θ₃)=0.671 2	m(θ₃)=0.859 6
	m(θ₁)=0.154 3	m(θ₁)=0.556 8	m(θ₁)=0.865 3	m(θ₁)=0.968 8
	m(θ₂)=0.746 9	m(θ₂)=0.356 2	m(θ₂)=0.089 1	m(θ₂)=0.015 6
Murphy方法
	m(θ₃)=0.098 8	m(θ₃)=0.078 2	m(θ₃)=0.038 2	m(θ₃)=0.012 7
		m(θ₁θ₃)=0.008 8	m(θ₁θ₃)=0.007 4	m(θ₁θ₃)=0.002 9
	m(θ₁)=0.154 3	m(θ₁)=0.650 0	m(θ₁)=0.930 5	m(θ₁)=0.984 6
	m(θ₂)=0.746 9	m(θ₂)=0.254 7	m(θ₂)=0.027 4	m(θ₂)=0.002 4
Deng方法
	m(θ₃)=0.098 8	m(θ₃)=0.085 8	m(θ₃)=0.033 9	m(θ₃)=0.009 8
		m(θ₁θ₃)=0.009 5	m(θ₁θ₃)=0.008 2	m(θ₁θ₃)=0.003 2
	m(θ₁)=0.073 3	m(θ₁)=0.658 1	m(θ₁)=0.939 1	m(θ₁)=0.985 9
	m(θ₂)=0.862 3	m(θ₂)=0.240 9	m(θ₂)=0.019	m(θ₂)=0.001 4
本文方法
	m(θ₃)=0.064 4	m(θ₃)=0.093 7	m(θ₃)=0.034 2	m(θ₃)=0.009 6
		m(θ₁θ₃)=0.007 3	m(θ₁θ₃)=0.007 7	m(θ₁θ₃)=0.003 1