D-S证据理论的不足及其数学修正

Shortcoming of D-S Evidence Theory and Its Mathematic Modification

针对D-S证据理论对高冲突证据融合得到有悖常理的无效结果问题,研究了国内外典型文献提出的各种改进方法,从原理上对其进行了组合规则的修正和证据源的修正两大分类,并对各种方法的不足进行了数理分析和总结.在此基础上引入证据信息容量和证据间距离函数来对各传感器提供的证据信息进行预处理,再对得到的新的证据信息用证据可信度作为权重进行加权融合.数值仿真实验表明:这种新的修正模型不但比较好地结合了两类改进方法的优点,在形式上和Dempster组合规则保持一致,而且能较好地处理冲突证据在信息交叉时的融合,取得了更加合理的效果,并且为D-S证据理论的完善提供了一个新的探索途径.

In allusion to counterintuitive conclusion produced by D-S theory of evidence, when it deals with high conflicting evidence, it was firstly studied the various improved methods of domestic and overseas typical documents, and classified them by D-S combination rule and the evidence source, analyzed and summarized the shortcoming of each method. On this foundation, ＂evidence information capacity＂ and ＂evidence distance function＂ were introduced into pretreating evidence information from various sensors,then ＂evidence credible function＂ was used as right-weight to fuse these new evidence information. The numerical simulation result shows that this new modification model not only combines the advantages of the two improved methods, but also can process better the fusion of conflict information in cross. This combination formula of the new modification model reaches better result and provides a new way to improve D-S theory of evidence.