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Issue:On a new approach to probability theory on MV-algebras

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Title of paper: On a new approach to probability theory on MV-algebras
Author(s):
Beloslav Riečan
Department of Mathematics, Faculty of Natural Sciences, Tajovskeho 40, 974 01 Banska Bystrica, Slovakia
Mathematical Institute of Slovak Academy of Sciences, Stefanikova 49, SK-81473 Bratislava
riecan@fpv.umb.sk
Presented at: 11th IWGN, Sofia, 5 December 2010
Published in: Conference proceedings, pages 57—65
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Abstract: The new approach permits to obtain better results, e.g. to ommit the usual assumption of the weak σ-distributivity of the considered MV-algebra. The main idea is in working with distribution function instead of morphisms of σ-algebras. The idea is based on some results concerning Kopka D-posets ([1], [5]), of course, in the MV-algebra case it is much more simple and better for applications. As an illustration of the method the law of large numbers is presented.


References:
  1. Kopka, F.: D-posets with meet function. Advances in Electrical Engineering 3, 2004, 34-36.
  2. Montagna, F.: An algebraic approach to propositional fuzzy logic. J. Logic Lang. Inf. 2000, 91-124.
  3. Mundici, D.: Interpretation of AFC*-algebras in Lukasiewicz sentential calculus. J. Funct. Anal 65, 1986, 15-63.
  4. Riečan B.: On the product MV-algebras. Tatra Mt. Math. Publ. 16, 1999, 143-149.
  5. Riečan, B., Lasova, L.: On the probability theory on the Kopka D-posets (to appear).
  6. Riečan, B., Mundici, D.: Probability on MV algebras, Handbook of Measue Theory, Elsevier, Amsterdam, 2002, 869-909.
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