论文标题
焦点及其对Möbius的含义转变和Dempster-Shafer理论
Focal points and their implications for Möbius Transforms and Dempster-Shafer Theory
论文作者
论文摘要
Dempster-Shafer理论（DST）概括了贝叶斯概率理论，提供了有用的其他信息，但遭受了更高的计算负担。已经完成了许多工作来减少信息融合与Dempster规则的时间复杂性，这是两个Zeta变换的点乘积，并且发现最佳的一般算法可以使这些转换的完整定义。然而，本文表明，Zeta变换及其逆变换可以完全简化，拟合信念函数中包含的信息数量。除此之外，此简化实际上适用于任何部分有序集合的任何功能。它依靠一个新的概念，即我们称为焦点，并且构成了Zeta和Möbius变换的最小领域。我们证明了这些一般结果对DST的兴趣，这不仅是为了减少信仰表示及其融合之间大多数转换的复杂性，而且出于理论目的。实际上，我们提供了证据和公式的结合分解的新概括，以发现每个分解权重如何与相应的质量函数相关联。
Dempster-Shafer Theory (DST) generalizes Bayesian probability theory, offering useful additional information, but suffers from a much higher computational burden. A lot of work has been done to reduce the time complexity of information fusion with Dempster's rule, which is a pointwise multiplication of two zeta transforms, and optimal general algorithms have been found to get the complete definition of these transforms. Yet, it is shown in this paper that the zeta transform and its inverse, the Möbius transform, can be exactly simplified, fitting the quantity of information contained in belief functions. Beyond that, this simplification actually works for any function on any partially ordered set. It relies on a new notion that we call focal point and that constitutes the smallest domain on which both the zeta and Möbius transforms can be defined. We demonstrate the interest of these general results for DST, not only for the reduction in complexity of most transformations between belief representations and their fusion, but also for theoretical purposes. Indeed, we provide a new generalization of the conjunctive decomposition of evidence and formulas uncovering how each decomposition weight is tied to the corresponding mass function.
