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摘要:
证据理论既能够灵活处理不确定信息, 包括随机性、模糊性、不准确性和不一致性, 又能够有效融合定量信息和定性知识. 目前, 证据理论已广泛应用于评估与决策等多个领域中, 包括多属性决策分析、信息融合、模式识别和专家系统等. 本文从D-S证据理论出发, 针对Dempster组合规则存在的“反直觉”问题和组合爆炸, 主要围绕置信分布理论系统地梳理了证据理论的发展过程, 总结分析了国内外典型文献, 最后从实际应用对证据理论进行了简要的评述和展望.
Abstract:Evidence theory can not only deal with uncertain information flexibly, including randomness, ambiguity, inaccuracy and inconsistency, but can integrate quantitative information and qualitative knowledge effectively. At present, evidence theory has been widely applied in various areas such as assessment and decision, involving multiple-attribute decision analysis, information fusion, pattern recognition, expert systems, and so on. Starting from the D-S evidence theory, this paper is focused on the counter-intuitive problem and the combinational explosion of the Dempster combination rule. The development process of evidence theory is systematically combed from the perspective of belief distribution, and typical literatures both here and abroad are summarized and analyzed. Finally, a brief commentary and outlook on evidence theory is given from its practical applications.
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Key words:
- Evidence theory /
- evidential reasoning /
- uncertainty /
- assessment and decision
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表 1 证据的基本概率分配
Table 1 Basic probability assignment of evidence
基本概率质量 犯罪嫌疑人 Peter Paul Mary ${m_1}$ 0.99 0.01 0 ${m_2}$ 0 0.01 0.99 
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表 2 证据的置信分布
Table 2 Belief distribution of evidence
证据 命题 $A$ $B$ ${e_1}$ 0.8 0.2 ${e_2}$ 0.4 0.6
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表 3 证据组合结果的比较
Table 3 Comparison of evidence combination results
组合规则 概率质量 $\emptyset $ $A$ $B$ $\Theta$ $P(\Theta )$ Dempster 组合规则 ${m_1}$ 0 0.1600 0.0400 0.8000 0 ${m_2}$ 0 0.3200 0.4800 0.2000 0 $\displaystyle\sum\nolimits_{C \cap D = \theta } \displaystyle{ {m_1}(C){m_2}(D)}$ 0.0896 0.3392 0.4112 0.1600 0 $m$ 0 0.3726 0.4517 0.1757 0 原始 ER 算法 ${m_1}$ 0 0.1600 0.0400 0 0.8000 ${m_2}$ 0 0.3200 0.4800 0 0.2000 ${m_{\theta ,e(2)}}$ 0 0.3726 0.4517 0 0.1757 ${p_{\theta ,e(2)}}$ 0 0.4520 0.5480 0 0 ER 规则 ${\widetilde m_1}$ 0 0.4000 0.1000 0 0.5000 ${\widetilde m_2}$ 0 0.2909 0.4364 0 0.2727 ${\widehat m_{\theta ,e(2)}}$ 0 0.1632 0.1272 0 0.0600 ${m_{\theta ,e(2)}}$ 0 0.4658 0.3630 0 0.1712 ${p_{\theta ,e(2)}}$ 0 0.5620 0.4380 0 0
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