北京邮电大学学报

  • EI核心期刊

北京邮电大学学报 ›› 2019, Vol. 42 ›› Issue (1): 28-34.doi: 10.13190/j.jbupt.2018-094

• 论文 • 上一篇    下一篇

基于规范分解的证据合成悖论分析

薛大为1, 王永2, 高康凯2   

  1. 1. 蚌埠学院 电子与电气工程学院, 蚌埠 233030;
    2. 中国科学技术大学 信息科学技术学院, 合肥 230027
  • 收稿日期:2018-05-08 出版日期:2019-02-28 发布日期:2019-03-08
  • 作者简介:薛大为(1976-),男,副教授,E-mail:bbxuedawei@163.com.
  • 基金资助:
    国家自然科学基金项目(61573332);安徽高校自然科学重点研究项目(KJ2018A0574)

Analysis of Evidence Combination Paradox Based on Canonical Decomposition

XUE Da-wei1, WANG Yong2, GAO Kang-kai2   

  1. 1. School of Electronics and Electrical Engineering, Bengbu University, Bengbu 233030, China;
    2. School of Information Science and Technology, University of Science and Technology of China, Hefei 230027, China
  • Received:2018-05-08 Online:2019-02-28 Published:2019-03-08

摘要: 利用Dempster合成规则组合证据时,有可能会出现合成悖论,且其表现形式多样,很难直接获得它们之间的规律或关系.对此,利用规范分解法将证据的基本信任分配转换为一组广义简单支持函数的组合形式.从2个典型反例分析入手,得出它们都存在信任忽略这一共同问题,在此基础上进一步总结出了Ⅰ类和Ⅱ类2种信任忽略形式及其发生的规律.对Ⅱ类信任忽略进一步分析,给出了不会发生Ⅱ类信任忽略的一般性结论.为更合理地使用Dempster合成规则避免出现合成悖论提供了依据,也为更有效地改进证据组合方法提供了参考.

关键词: 证据理论, Dempster合成规则, 合成悖论, 规范分解, 信任忽略

Abstract: When applying Dempster's rule of combination to fuse pieces of evidence, a combination paradox can occur. It is very difficult to acquire the law or relationship among these combination paradoxes with some different manifestations. In order to resolve this problem, the study is carried out by the aid of canonical decomposition which is used to transform the basic belief assignment into the combination of a set of generalized simple support function. Firstly, two typical counterexamples are analyzed, and then the common characteristic between them, neglecting belief, is summarized. On the basis of this, a further analysis is made. Two forms of neglecting belief and the rules of causing them are generalized. A further analysis of type Ⅱ neglecting belief is made. Some general conclusions,that type Ⅱ neglecting belief cannot occur,are presented. These generalized rules and conclusions provide not only the basis for applying Dempster's rule more reasonably to avoid combination paradoxes, but also the reference for modifying the combination method more effectively.

Key words: evidence theory, Dempster's rule of combination, combination paradox, canonical decomposition, neglecting belief

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