A Simple Proportional Conflict Redistribution Rule
A Simple Proportional Conflict Redistribution Rule
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发表时间：
2004-08
影响因子：
0.2
通讯作者：
F. Smarandache;J. Dezert
中科院分区：
文献类型：
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作者：
F. Smarandache;J. Dezert
有人提出了 Josang、Daniel 和 Vannoorenberghe 最近提出的 WAO（加权平均算子）的第一个替代组合规则，称为比例冲突重新分配规则（表示为 PCR1）。 PCR1 和 WAO 是 WO（加权算子）的特殊情况，因为冲突的质量会根据某些权重因子重新分配。在第一个 PCR 规则中，每个非空集相对于其相应质量矩阵的非零和进行比例化，而不是像 WAO 中那样对其质量列平均值进行，但结果与 Ph. Smets 指出的相同。此外，我们将WAO（这里没有给出解）扩展到当所有非空集合的所有列和为零时的简并情况，然后将冲突质量转移到所有非空集合的非空析取形式；但如果这种析取形式碰巧是空的，那么我们就会考虑一个开放的世界（即辨别框架可能包含新的假设），因此所有冲突的质量都会转移到空集。除了WAO之外，我们还提出了PCR1的通用公式（WAO适用于非退化情况）。还提供了几个数值示例以及与文献中发表的证据组合的其他规则的比较。这些替代规则之间的另一个区别是，WAO 是在幂集上定义的，而 PCR1 是在超幂集（戴德金格）上定义的。 PCR1 的一个很好的特性是，它不仅适用于非简并情况，也适用于动态融合中出现的简并情况，而 WAO 在这种情况下给出的质量总和小于 1（WAO 在这些情况下不起作用）。同时我们表明，不幸的是，PCR1 和 WAO 在融合过程中并没有保留空洞信念分配的中立性。然而，这一严重缺陷可以通过配套论文中提出的新 PCR 规则轻松规避。
One proposes a first alternative rule of combination to WAO (Weighted Average Operator) proposed recently by Josang, Daniel and Vannoorenberghe, called Proportional Conflict Redistribution rule (denoted PCR1). PCR1 and WAO are particular cases of WO (the Weighted Operator) because the conflicting mass is redistributed with respect to some weighting factors. In this first PCR rule, the proportionalization is done for each non-empty set with respect to the non-zero sum of its corresponding mass matrix - instead of its mass column average as in WAO, but the results are the same as Ph. Smets has pointed out. Also, we extend WAO (which herein gives no solution) for the degenerate case when all column sums of all non-empty sets are zero, and then the conflicting mass is transferred to the non-empty disjunctive form of all non-empty sets together; but if this disjunctive form happens to be empty, then one considers an open world (i.e. the frame of discernment might contain new hypotheses) and thus all conflicting mass is transferred to the empty set. In addition to WAO, we propose a general formula for PCR1 (WAO for non-degenerate cases). Several numerical examples and comparisons with other rules for combination of evidence published in literature are presented too. Another distinction between these alternative rules is that WAO is defined on the power set, while PCR1 is on the hyper-power set (Dedekind’s lattice). A nice feature of PCR1, is that it works not only on non-degenerate cases but also on degenerate cases as well appearing in dynamic fusion, while WAO gives the sum of masses in this cases less than 1 (WAO does not work in these cases). Meanwhile we show that PCR1 and WAO do not preserve unfortunately the neutrality property of the vacuous belief assignment though the fusion process. This severe drawback can however be easily circumvented by new PCR rules presented in a companion paper.