16-17 May 2019 • Sofia, Bulgaria

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

Issue:Uncertainty inspired by economical models

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Title of paper: Uncertainty inspired by economical models
Author(s):
Alžbeta Michalíková
Department of Informatics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 97401 Banská Bystrica, Slovakia
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Beloslav Riečan
Department of Informatics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 97401 Banská Bystrica, Slovakia
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Published in: "Notes on IFS", Volume 20, 2014, Number 2, pages 69-74
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Abstract: Some applications of the sets theory in economical problems are presented. Especially the generalized Choquet and Šipoš’s integrals are exposed. We present two possibilities how to extend mathematical models of the problem. The first is the Atanassov intuitionistic fuzzy sets theory for the domain, the second one is the Riesz vector space theory for the range of considered mappings.
Keywords: Prospect theory, Šipoš integral, IF-sets.
AMS Classification: 03E72, 03E10
References:
  1. Atanassov, K., Intuitionistic Fuzzy Sets: Theory and Applications, Springer Physica–Verlag, Heidelberg, 1999.
  2. Boccuto, A., B. Riečan, M. Vrábelová, Kurzweil–Henstock Integral in Riesz Spaces. Betham Books, 2009.
  3. Choquet, G., Lectures on Analysis, Benajmin, New York, 1969.
  4. Kahneman, D., A. Tversky, Prospect theory: An analysis of decision under risk. Econometrica. Vol. XLVII, 1979, 26–291.
  5. Kolmogorov, A. N., Basic Notions of the Probability Theory, Moskow, Nauka, 1933 (in Russian).
  6. Mundici, D. Interpretation of AFC*-algebras in Łukasiewicz sentential calculus. J. Funct. Anal., Vol. 65, 1986, 15–63.
  7. Riečan, B., D. Mundici, Probability on MV-algebras. – In: Handbook of Measure Theory(E. Pap ed.), Elsevier, Amsterdam, 2002, 869–909.
  8. Riečan, B., T. Neubrunn, Integral, Measure, and Ordering, Kluwer, Amsterdam, 1997
  9. Schmidt, E., J. Kaczprzyk, Intuitionistic fuzzy sets in some medical applications. Notes on Intuitionistic Fuzzy Sets, Vol. 7, 2004, No. 4, 58–64.
  10. Šipoš, J., Integral with respect to a pre-measure. Math. Slovaca, Vol. 219, 1979, 141–155.
  11. Šipoš, J., Non linear integrals. Math. Slovaca, Vol. 29, 1979, 257–270.
  12. Zadeh, L. A., Fuzzy sets. Informations and Control, Vol. 8, 1965, 338–358.
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