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Generic and Concurrent Computation of Belief Combination Rules

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Data Management Technologies and Applications (DATA 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 737))

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Abstract

As a form of random set, belief functions come with specific semantic and combination rule able to perform the representation and the fusion of uncertain and imprecise informations. The development of new combination rules able to manage conflict between data now offers a variety of tools for robust combination of piece of data from a database. The computation of multiple combinations from many querying cases in a database make necessary the development of efficient approach for concurrent belief computation. The approach should be generic in order to handle a variety of fusion rules. We present a generic implementation based on a map-reduce paradigm. An enhancement of this implementation is then proposed by means of a Markovian decomposition of the rule definition. At last, comparative results are presented for these implementations within the frameworks Apache Spark and Apache Flink.

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Author information

Authors and Affiliations

  1. DGA MI/Lab-STICC, UMR CNRS 6285, Ensta Bretagne, 2 rue François Verny, Brest, France

    Frédéric Dambreville

Authors
  1. Frédéric Dambreville
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Corresponding author

Correspondence to Frédéric Dambreville .

Editor information

Editors and Affiliations

  1. Department of Electronics and Information, Politecnico di Milano, Milan, Italy

    Chiara Francalanci

  2. School of Computing, Dublin City University, Dublin, Ireland

    Markus Helfert

A Rules Definitions

A Rules Definitions

1.1 A.1 Dubois & Prade Rule

The rule proposed by Dubois and Prade extends the conjunctive rule by redistributing disjunctively the conflict:

$$\begin{aligned} m_1\oplus _{DP}m_2(X)= & {} \sum _{Y_1,Y_2:\left\{ \begin{array}{c} Y_1\cap Y_2 \ne \emptyset \\ Y_1\cap Y_2=X \end{array}\right. }m_1(Y_1)m_2(Y_2) \\\nonumber&+ \sum _{Y_1,Y_2:\left\{ \begin{array}{c} Y_1\cap Y_2 = \emptyset \\ Y_1\cup Y_2=X \end{array}\right. }m_1(Y_1)m_2(Y_2) . \end{aligned}$$
(20)

1.2 A.2 PCR6 Rule

The rule proposed by Martin and Osswald extends the conjunctive rule by a local proportional redistribution of the conflict:

(21)

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Dambreville, F. (2017). Generic and Concurrent Computation of Belief Combination Rules. In: Francalanci, C., Helfert, M. (eds) Data Management Technologies and Applications. DATA 2016. Communications in Computer and Information Science, vol 737. Springer, Cham. https://doi.org/10.1007/978-3-319-62911-7_7

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  • DOI: https://doi.org/10.1007/978-3-319-62911-7_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62910-0

  • Online ISBN: 978-3-319-62911-7

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