有效的莫比乌斯变换及其在Dempster-Shafer理论中的应用：澄清和实现
Efficient Möbius Transformations and their applications to Dempster-Shafer Theory: Clarification and implementation
摘要：
Dempster-Shafer理论（DST）推广了贝叶斯概率理论，提供了有用的额外信息，但具有很高的计算负担。为了降低Dempster规则信息融合中计算的复杂性，人们做了大量工作。主要的方法利用布尔格的结构或信念源中包含的信息。每一个都有它的优点取决于情况。在本文中，我们提出了一系列的图形的zeta和莫比乌斯变换的计算，最佳地利用分配半格的结构和所包含的信息的信念来源。我们称之为有效莫比乌斯变换（EMT）。我们表明，EMT的复杂性总是低于算法的复杂性，考虑整个格，如快速莫比乌斯变换（FMT）的所有DST变换。然后，我们解释如何使用它们来融合两个信念来源。更一般地说，我们的EMT适用于任何有限分配格中的任何函数，专注于满足闭或连接闭子集。本文扩展了我们在可扩展不确定性管理（SUM）国际会议上发表的工作。它澄清了它，带来了一些小的更正，并提供了实现细节，如数据结构和算法应用于DST。
英文摘要：
Dempster-Shafer Theory (DST) generalizes Bayesian probability theory, offering useful additional information, but suffers from a high computational burden. A lot of work has been done to reduce the complexity of computations used in information fusion with Dempster's rule. The main approaches exploit either the structure of Boolean lattices or the information contained in belief sources. Each has its merits depending on the situation. In this paper, we propose sequences of graphs for the computation of the zeta and Möbius transformations that optimally exploit both the structure of distributive semilattices and the information contained in belief sources. We call them the Efficient Möbius Transformations (EMT). We show that the complexity of the EMT is always inferior to the complexity of algorithms that consider the whole lattice, such as the Fast Möbius Transform (FMT) for all DST transformations. We then explain how to use them to fuse two belief sources. More generally, our EMTs apply to any function in any finite distributive lattice, focusing on a meet-closed or join-closed subset. This article extends our work published at the international conference on Scalable Uncertainty Management (SUM). It clarifies it, brings some minor corrections and provides implementation details such as data structures and algorithms applied to DST.
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。
