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An algebraic treatment of imprecise probabilities

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Języki publikacji
EN
Abstrakty
EN
This is a survey paper about an algebraic approach to imprecise probabilities. In the first part of it, we outline the work by Walley on imprecise probabilities and the more algebraic approach of Fedel et al.. Then, in the second part we will present some work in progress about a general treatment of upper and lower probabilities over many-valued events and of upper and lower previsions of gambles, by means of Universal Algebra.
Słowa kluczowe
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Rocznik
Strony
497--509
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
  • Deparment Of Mathematics And Computer Science "R. Magari" University Of Siena Pian Dei Mantellini 44 53100 Siena, Italy, montagna@unisi.it
Bibliografia
  • [1] B. Anger, J. Lembcke, Infinite subadditive capacities as upper envelopes of measures, Zeitschrift für Wahrscheinlichkeitstheorie 68 (1985), 403–414.
  • [2] A. Bigard, K. Keimel, S. Wolfenstein, Groupes et Anneaux Réticulés, Lecture Notes in Math. 608 (1977), Springer Verlag.
  • [3] S. Bova, F. Flaminio, The coherence of Łukasiewicz assessments is NP-complete, Internat. J. Approx. Reason. 51(3) (2010), 294–304.
  • [4] B. de Finetti, Theory of Probability, vol. I. John Wiley and Sons, Chichester, 1974.
  • [5] M. Fedel, K. Keimel, F. Montagna, W. Roth, Imprecise probabilities, bets and functional analytic methods in Łukasiewicz logic, submitted.
  • [6] T. Flaminio, F. Montagna, MV-algebras with internal states and probabilistic fuzzy logics, Internat. J. Approx. Reason. 50 (2009), 138–152.
  • [7] P. Hájek, Metamathematics of Fuzzy Logic, Kluwer, Dordrecht, 1998.
  • [8] J. Y. Halpern, Reasoning about Uncertainty, MIT Press, 2003.
  • [9] T. Kroupa, Every state on a semisimple MV algebra is integral , Fuzzy Sets and Systems 157(20) (2006), 2771–2782.
  • [10] D. Mundici, Interpretation of AF C*-algebras in Łukasiewicz sentential calculus, J. Funct. Anal. 65 (1986), 15–63.
  • [11] D. Mundici, Averaging the truth value in Łukasiewicz logic, Studia Logica 55(1) (1995), 113–127.
  • [12] D. Mundici, Bookmaking over infinite-valued events, Internat. J. Approx. Reason. 46 (2006), 223–240.
  • [13] G. Panti, Invariant measures in free MV algebras, Comm. Algebra 36 (2008), 2849–2861. Available at Arxiv preprint math. LO/0508445, 2005.
  • [14] W. Rudin, Functional Analysis, 2nd Edition, McGraw-Hill Publ., 1991.
  • [15] P.Walley, Statistical Reasoning with Imprecise Probabilities, Volume 42 of Monographs on Statistics and Applied Probability, Chapman and Hall, London 1991.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA4-0033-0014
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