新的证据冲突度量方法
Novel approach for measuring the conflict between evidence

为了解决证据理论在处理高度冲突证据时会出现的失效问题, 研究了证据冲突的度量和表示方法. 首先, 证据距离作为一种主要的证据冲突度量方法, 通过分析各种证据距离的不足, 定义一种新的概率距离, 并结合 Jousselme距离来描述证据之间的差异性. 其次, 由于证据距离无法完全代表证据冲突, 根据模糊交叉熵的概念, 定 义了基本概率指派(basic probability assignment, BPA)交叉熵来表示证据之间的散度. 再次, 通过Hamacher T–余范融 合证据距离和证据散度两个方面, 提出一种新的证据冲突度量方法. 最后用数值算例验证了该方法的有效性.
To solve the invalidation problems when the evidence theory is used to deal with the cases with highly conflicting evidence, a new method is investigated for measuring and representing the degree of conflict between evidence. First of all, based on the comparison and analysis of some existing evidence distance methods which are the main conflict measures, a new probabilistic-based distance is defined and combined with Jousselme’s distance to describe the difference between evidence. Next, because the conception of evidence distance cannot substitute for the definition of evidential conflict completely, a cross entropy of basic probability assignments (BPAs) is proposed based on the idea of fuzzy cross entropy to present the degree of divergence between evidence. Then, in the light of mixing the distance and divergence between evidence by applying Hamacher T-conorm, a new method for measuring the degree of conflict between evidence is put forward. Finally, the numerical examples verify the efficiency of the proposed method.