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Finitely Additive Probability Measures in Automated Medical Diagnostics

  • Milica Knežević
  • Zoran Ognjanović
  • Aleksandar Perović
Part of the Communications in Computer and Information Science book series (CCIS, volume 443)

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.

Keywords

probability measures classification fuzzy logic soft computing medical diagnosis 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Milica Knežević
    • 1
  • Zoran Ognjanović
    • 1
  • Aleksandar Perović
    • 2
  1. 1.Mathematical Institute of the Serbian Academy of Sciences and ArtsBelgradeSerbia
  2. 2.Faculty of Transport and Traffic EngineeringUniversity of BelgradeBelgradeSerbia

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