Issue:Uncertainty inspired by economical models

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http://ifigenia.org/wiki/issue:nifs/20/2/69-74

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 alzbeta.michalikova@umb.sk Beloslav Riečan Department of Informatics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 97401 Banská Bystrica, Slovakia beloslav.riecan@umb.sk Published in: "Notes on IFS", Volume 20, 2014, Number 2, pages 69-74 Download:  PDF (147  Kb, File info) 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: Atanassov, K., Intuitionistic Fuzzy Sets: Theory and Applications, Springer Physica–Verlag, Heidelberg, 1999. Boccuto, A., B. Riečan, M. Vrábelová, Kurzweil–Henstock Integral in Riesz Spaces. Betham Books, 2009. Choquet, G., Lectures on Analysis, Benajmin, New York, 1969. Kahneman, D., A. Tversky, Prospect theory: An analysis of decision under risk. Econometrica. Vol. XLVII, 1979, 26–291. Kolmogorov, A. N., Basic Notions of the Probability Theory, Moskow, Nauka, 1933 (in Russian). Mundici, D. Interpretation of AFC*-algebras in Łukasiewicz sentential calculus. J. Funct. Anal., Vol. 65, 1986, 15–63. Riečan, B., D. Mundici, Probability on MV-algebras. – In: Handbook of Measure Theory(E. Pap ed.), Elsevier, Amsterdam, 2002, 869–909. Riečan, B., T. Neubrunn, Integral, Measure, and Ordering, Kluwer, Amsterdam, 1997 Schmidt, E., J. Kaczprzyk, Intuitionistic fuzzy sets in some medical applications. Notes on Intuitionistic Fuzzy Sets, Vol. 7, 2004, No. 4, 58–64. Šipoš, J., Integral with respect to a pre-measure. Math. Slovaca, Vol. 219, 1979, 141–155. Šipoš, J., Non linear integrals. Math. Slovaca, Vol. 29, 1979, 257–270. Zadeh, L. A., Fuzzy sets. Informations and Control, Vol. 8, 1965, 338–358. Citations: The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.