Issue:Probability on interval valued events

{{issue/data | conference     = 11{{sup|th}} IWGN, Sofia, 5 December 2010 | issue          = Conference proceedings, pages 43—47 | file           = IWGN-2010-43-47.pdf | format         = PDF | size           = 155 | abstract       = Interval valued events are considered, i.e. pairs A = (&mu;{{sub|A}}, &nu;{{sub|A}}) of measurable mappings &mu;{{sub|A}}, &nu;{{sub|A}} : (&Omega;, S) → [0, 1] such that &mu;{{sub|A}} &le; &nu;{{sub|A}}. In the paper the probability is considered a mapping p : F → [&prime;, &infin;] 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. | keywords       = | references     = | citations      = | see-also       = }}
 * 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.