16-17 May 2019 • Sofia, Bulgaria

Submission: 21 February 2019Notification: 11 March 2019Final Version: 1 April 2019

Issue:On the Lebesgue IF–measure

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Title of paper: On the Lebesgue IF–measure
Author(s):
Alžbeta Michalíková
Department of Computer Science Faculty of Natural Sciences, Matej Bel University, 40 Tajovského Str., 974 01 Banská Bystrica, Slovakia
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Beloslav Riečan
Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01 Banská Bystrica
Mathematical Institute of Slovak Acad. of Sciences, Štefánikova 49, Bratislava, Slovakia
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Presented at: 21st International Conference on Intuitionistic Fuzzy Sets, 22–23 May 2017, Burgas, Bulgaria
Published in: "Notes on IFS", Volume 23, 2017, Number 2, pages 8—12
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Abstract: An IF-state on the family of IF-subsets of the unit interval is constructed invariant under shifts.
Keywords: IF-sets, IF-states, Invariant measures.
AMS Classification: 03E72.
References:
  1. Atanassov, K. (1999). Intuitionistic Fuzzy Sets: Theory and Applications. Physic Verlag, Heidelberg.
  2. Ciungu, L., & Riečan, B. (2009). General form of probabilities on IF-sets. In: Fuzzy Logic and Applications. Proc. WILF Palermo 2009, 101–107.
  3. Ciungu L., Riečan B. (2010). Representation theorem for probabilities on IFS-events. Information Sciences, 180, 793–798.
  4. Halmos, P. R. (1950). Measure Theory. Van Nostrand, New York.
  5. Riečan, B. (2006). On a problem of Radko Mesiar: General form of IF-probabilities. Fuzzy Sets and Systems, 152, 1485–1490.
  6. Riečan, B. (2012). Analysis of Fuzzy LogicModels. In: Intelligent Systems (ed. V. Koleshko) INTECH 2012, 217–244.
  7. Zadeh, L. (1965). Fuzzy Sets. Inform. and Control, 8, 338–358.
  8. Zadeh, L. (1968). Probability measures of fuzzy events. J. Math. Anal. Appl., 23, 421– 427.
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