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Finitely Additive Probability Measures in Automated Medical Diagnostics

  • Conference paper
Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2014)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 443))

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Abstract

We describe one probabilistic approach to classification of a set of objects when a classification criterion can be represented as a propositional formula. It is well known that probability measures are not truth functional. However, if μ is any probability measure and α is any propositional formula, μ(α) is uniquely determined by the μ-values of conjunctions of pairwise distinct propositional letters appearing in α. In order to infuse truth functionality in the generation of finitely additive probability measures, we need to find adequate binary operations on [0,1] that will be truth functions for finite conjunctions of pairwise distinct propositional letters. The natural candidates for such truth functions are t-norms. However, not all t-norms will generate a finitely additive probability measure. We show that Gödel’s t-norm and product t-norm, as well as their linear convex combinations, can be used for the extension of any evaluation of propositional letters to finitely additive probability measure on formulas. We also present a software for classification of patients with suspected systemic erythematosus lupus (SLE), which implements the proposed probabilistic approach.

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Author information

Authors and Affiliations

  1. Mathematical Institute of the Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000, Belgrade, Serbia

    Milica Knežević & Zoran Ognjanović

  2. Faculty of Transport and Traffic Engineering, University of Belgrade, Vojvode Stepe 305, 11000, Belgrade, Serbia

    Aleksandar Perović

Authors
  1. Milica Knežević
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  2. Zoran Ognjanović
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  3. Aleksandar Perović
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Editor information

Editors and Affiliations

  1. University Montpellier 2, LIRMM - CNRS UMR 5506, 161, Rue Ada, 34392, Montpellier Cedex 5, France

    Anne Laurent

  2. LIRMM, UMR CNRS/Universite Montpellier II, 161 rue Ada, 34392, Montpellier cedex 5, France

    Olivier Strauss

  3. UPMC Univ. Paris 06, CNRS UMR 7606, LIP6, F-75005, Paris, France

    Bernadette Bouchon-Meunier

  4. Dept. of Information Systems, Iona College, 710 North Ave, 10801, New Rochelle, NY, USA

    Ronald R. Yager

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Knežević, M., Ognjanović, Z., Perović, A. (2014). Finitely Additive Probability Measures in Automated Medical Diagnostics. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2014. Communications in Computer and Information Science, vol 443. Springer, Cham. https://doi.org/10.1007/978-3-319-08855-6_2

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  • DOI: https://doi.org/10.1007/978-3-319-08855-6_2

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08854-9

  • Online ISBN: 978-3-319-08855-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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