Mobius变换的计算方面
Computational Aspects of the Mobius Transform
摘要：
在本文中，我们与每一个（有向）图G的变换称为Mobius变换的图G。图（O）的Mobius变换对于Dempster-Shafer证据理论具有重要意义。然而，由于它是计算非常繁重，莫比乌斯变换与Dempster的规则组合是一个主要的障碍，使用Dempster-Shafer理论处理专家系统中的不确定性。本文的主要贡献是发现了（O）的“快速Mobius变换”。这些“快速莫比乌斯变换”是计算（O）的莫比乌斯变换的最快算法。作为一个简单而有用的应用，我们提供了一个算法，通过公共功能，计算Dempster的组合规则，这是比通常的快得多。
英文摘要：
In this paper we associate with every (directed) graph G a transformation called the Mobius transformation of the graph G. The Mobius transformation of the graph (O) is of major significance for Dempster-Shafer theory of evidence. However, because it is computationally very heavy, the Mobius transformation together with Dempster's rule of combination is a major obstacle to the use of Dempster-Shafer theory for handling uncertainty in expert systems. The major contribution of this paper is the discovery of the 'fast Mobius transformations' of (O). These 'fast Mobius transformations' are the fastest algorithms for computing the Mobius transformation of (O). As an easy but useful application, we provide, via the commonality function, an algorithm for computing Dempster's rule of combination which is much faster than the usual one.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
