Finitely Additive Probability Measures in Automated Medical Diagnostics

• Published in: Information Processing and Management of Uncertainty in Knowledge-Based Systems pp. 10 - 19
• Main Authors: Knežević, Milica, Ognjanović, Zoran, Perović, Aleksandar
• Format: Book Chapter
• Language: English
• Published: Cham Springer International Publishing 2014
• Series: Communications in Computer and Information Science
• Subjects: classification; fuzzy logic; medical diagnosis; probability measures; soft computing
• ISBN: 3319088548; 9783319088549
• ISSN: 1865-0929; 1865-0937
• DOI: 10.1007/978-3-319-08855-6_2

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.