Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient M\"obius Transformations and their applications to
  Dempster-Shafer Theory: Clarification and implementation   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 M\"obius
transformations that optimally exploit both the structure of distributive
semilattices and the information contained in belief sources. We call them the
Efficient M\"obius 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 M\"obius 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.

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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex