In this paper, we prove that any dichotomous basic belief assignment (BBA) m can be expressed as the combination of two simple belief assignments m p and m c called, respectively, the pros and cons BBAs thanks to the proportional conflict redistribution rule no 5 (PCR5). This decomposition always exists and is unique and we call it the canonical decomposition of the BBA m . We also show that canonical decompositions do not exist in general if we use the conjunctive rule, the disjunctive rule, Dempster's rule, Dubois and Prade's or Yager's rules, or even the averaging rule of combination. We give some numerical examples of canonical decompositions and discuss of the potential interest of this canonical decomposition for applications in information fusion.

中文翻译：

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二分基本信念分配的规范分解

在本文中，我们证明了任何二分基本信念分配 (BBA) m 都可以表示为两个简单信念分配 mp 和 mc 的组合，这两个简单的信念分配分别称为优点和缺点 BBA，这要归功于比例冲突再分配规则 5 (PCR5 ）。这种分解始终存在并且是唯一的，我们称其为 BBA m 的规范分解。我们还表明，如果我们使用合取规则、析取规则、登普斯特规则、Dubois 和 Prade 或 Yager 规则，甚至组合的平均规则，则规范分解一般不存在。我们给出了一些典型分解的数值例子，并讨论了这种典型分解在信息融合中的应用的潜在兴趣。