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Issue:Probability on interval valued events

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http://ifigenia.org/wiki/issue:iwgn-2010-43-47
Title of paper: Probability on interval valued events
Author(s):
Beloslav Riečan
Institute of Mathemathics and Computer Science UMB and MU SAV, Dumbierska 1, 974 11 Banska Bystrica, Slovakia
Department of Mathematics, Faculty of Natural Sciences, Tajovskeho 40, 974 01 Banska Bystrica, Slovakia
riecan@fpv.umb.sk
Pavol Kral
Institute of Mathemathics and Computer Science UMB and MU SAV, Dumbierska 1, 974 11 Banska Bystrica, Slovakia
Department of Quantitative Methods and Information Systems, Faculty of Economic, Tajovskeho 10, 975 90 Banska Bystrica, Slovakia
pavol.kral@umb.sk
Presented at: 11th IWGN, Sofia, 5 December 2010
Published in: Conference proceedings, pages 43—47
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Abstract: Interval valued events are considered, i.e. pairs A = (μA, νA) of measurable mappings μA, νA : (Ω, S) → [0, 1] such that μA ≤ νA. In the paper the probability is considered a mapping p : F → [′, ∞] defined on the family F of all interval valued events. The paper contains two main main results. The first result is the probability representation theorem. The second one is an embedding into an MV-algebra, hence the well developed MV-algebra probability theory can be applied to the interval valued probability theory.


References:
  1. Zadeh, L.: Probability measures of fuzzy events. Journal of Mathematical analysis and applications 23 (2), 1968, 421{427.
  2. Dvurečenskij, A., Pulmannov, S.: New trends in quantum structures. Kluwer Academic Publishers, Ister Science, Bratislava, 2000.
  3. Riečan, B., Mundici D.: Probability on MV-algebras. In: Handbook of Measure Theory. Elsevier. Amsterdam 2002, 869{909.
  4. Riečan, B.: Probability theory on IF events. In: Algebraic and Proof-Theoretic Aspects of Non-classical logics. Papers in Honor of Daniele Mundici on the Occasion of his 60th Birthday. Lecture Notes in Computer Science (Aguzzoli, S. et. al. eds.), Springer, Berlin, 2007, 209 - 308.
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