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From Sensors to Dempster-Shafer Theory and Back: The Axiom of Ambiguous Sensor Correctness and Its Applications

Keynote at DEXA’2020 – The 31st International Conference on Database and Expert Systems Applications

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Database and Expert Systems Applications (DEXA 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12391))

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Abstract

Since its introduction in the 1960s, Dempster-Shafer theory became one of the leading strands of research in artificial intelligence with a wide range of applications in business, finance, engineering and medical diagnosis. In this paper, we aim to grasp the essence of Dempster-Shafer theory by distinguishing between ambiguous-and-questionable and ambiguous-but-correct perceptions. Throughout the paper, we reflect our analysis in terms of signals and sensors as a natural field of application. We model ambiguous-and-questionable perceptions as a probability space with a quantity random variable and an additional perception random variable (Dempster model). We introduce a correctness property for perceptions. We use this property as an axiom for ambiguous-but-correct perceptions. In our axiomatization, Dempster’s lower and upper probabilities do not have to be postulated: they are consequences of the perception correctness property. Even more, we outline how Dempster’s lower and upper probabilities can be understood as best possible estimates of quantity probabilities. Finally, we define a natural knowledge fusion operator for perceptions and compare it with Dempster’s rule of combination.

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Notes

  1. 1.

    Note, that standard the notation for random variables applies throughout all the paper, i.e., given a random variables \(X : \omega \longrightarrow I\), we have that Expr(X) denotes the event \(\{ \omega \, | \, Expr(X(\omega )) \}\) for each common mathematical expression \(Expr(\_ {\!}\_)\). For example, \((X=y)\) stands for \(X^{-1}(y)=\{ \omega \, | X(\omega )=y \}\) as usual; \(X \subseteq A\) stands for \(\{ \omega \, | X(\omega ) \subseteq A \}\); \(A \subset X\) stands for \(\{ \omega \, | A \subset X(\omega )\}\) etc.

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Author information

Authors and Affiliations

  1. Information Systems Group, Tallinn University of Technology, Akadeemia tee 15a, 12618, Tallinn, Estonia

    Dirk Draheim

  2. Applied Artificial Intelligence Group, Tallinn University of Technology, Akadeemia tee 15a, 12618, Tallinn, Estonia

    Tanel Tammet

Authors
  1. Dirk Draheim
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  2. Tanel Tammet
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Correspondence to Dirk Draheim .

Editor information

Editors and Affiliations

  1. Clausthal University of Technology, Clausthal-Zellerfeld, Germany

    Sven Hartmann

  2. Johannes Kepler University of Linz, Linz, Austria

    Josef Küng

  3. Johannes Kepler University of Linz, Linz, Austria

    Gabriele Kotsis

  4. IFS, Vienna University of Technology, Vienna, Wien, Austria

    A Min Tjoa

  5. Johannes Kepler University of Linz, Linz, Austria

    Ismail Khalil

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Draheim, D., Tammet, T. (2020). From Sensors to Dempster-Shafer Theory and Back: The Axiom of Ambiguous Sensor Correctness and Its Applications. In: Hartmann, S., Küng, J., Kotsis, G., Tjoa, A.M., Khalil, I. (eds) Database and Expert Systems Applications. DEXA 2020. Lecture Notes in Computer Science(), vol 12391. Springer, Cham. https://doi.org/10.1007/978-3-030-59003-1_1

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  • DOI: https://doi.org/10.1007/978-3-030-59003-1_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-59002-4

  • Online ISBN: 978-3-030-59003-1

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