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Issue:On the probability on IF-sets and MV-algebras

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Title of paper: On the probability on IF-sets and MV-algebras
Author(s):
Beloslav Riečan
Faculty of Natural Sciences, Matej Bel University, Department of Mathematics, Tajovskeho 40, 974 01 Banska Bystrica, SLOVAKIA
Mathematical Institute of Slovak Acad. of Sciences, Stefanikova 49, SK-81473 Bratislava, SLOVAKIA
riecan@mat.savba.skriecan@fpv.umb.sk
Presented at: 1st International Workshop on Intuitionistic Fuzzy Sets, 22 September 2005, Banská Bystrica, Slovakia
Published in: "Notes on IFS", Volume 11 (2005), Number 6, pp. 21-25
Download:  PDF (2263  Kb, File info)
Abstract: Starting with a family F of IF-events we present a simple construction of an MV-algebra M such that F can be embedded to M. Moreover, there is a one-to-one correspondence between probabilities on F and M.
Keywords: IF-sets, outer measure, measurable element.
References:
  1. Atanassov, K.: Intuitionistic Fuzzy Sets: Theory and Applications. Physica Verlag, New York 1999.
  2. Cignoli, L. O., D'Ottaviano, M. L., Mundici, D.: Algebraic Foundations of Many-valued reasoning. Kluwer Academic Publishers, Dordrecht 2000.
  3. Deschrivjer, G. - Cornells, Ch. - Kerre, E.E.: Triangle and square: a comparison. Proc. Tenth Int. Conf. IPMU, Perugia, Italy 2004, 1389 - 1395.
  4. Grzegorzewski, P. - Mrowka, E.: Probability of intuitionistic fuzzy events. In: Soft Methods in Probability, Statistics and Data Analysis (P. Grzegorzewski et al. eds.). Physica Verlag, New York 2002, 105 - 115.
  5. Lendelova, K. - Michalfkova, A. - Riecan, B.: Representation of probability on triangle. In: Proc. WISCC - 4'04, in print.
  6. Riecan, B.: A descriptive definition of the probability on intuitionistic fuzzy sets. In: Proc. EUSFLAT'2003 (Wagenecht, M. and Hampet, R. eds.), Zittau - Goerlitz Univ. Appl. Sci, Dordrecht 2000, 263 - 266.
  7. Riecan, B.: Representation of probabilities on IFS events. Advances in Soft Computing, Soft Methodology and Random Information Systems (M. Lopez - Diaz et al. Springer, Berlin 2004, 243 - 246.
  8. Riecan, B.: On a problem of Radko Mesiar. Fuzzy Sets and Systems. Accepted.
  9. Riecan, B.: On the entropy on the Lukasiewicz square. Proc. Joint EUSFLAT - LFA 2005, Barcelona, 330 - 333.
  10. Riecan, B.: On the entropy of IF dynamical systems. In: IWIFSGN'2005, Warsaw, Poland, in print.
  11. Riecan, B. - Mundici, D.: Probability on MV-algebras. In: Handbook on Measure Theory (E.Pap ed.), Elsevier, Amsterdam 2002.
  12. Riecan, B. - Neubrunn, T.: Integral, Measure, and Ordering. Kluwer, Dordrecht 1997.
  13. Schmidt E. - Kacprzyk J.: Probability of intuitionistic fuzzy events and their applications in decision making. Proc. of EUSFLAT'99, Palma de Mallorca 1999, 457 - 460.
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