Title of paper:

On IFnumbers

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, SK81473 Bratislava, SLOVAKIA

riecanumb.sk

Daniela Kluvancová

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, SK81473 Bratislava, SLOVAKIA

kluvancova.danielaumb.sk


Presented at:

20th International Conference on Intuitionistic Fuzzy Sets, 2–3 September 2016, Sofia, Bulgaria

Published in:

"Notes on IFS", Volume 22, 2016, Number 3, pages 9—13

Download:

PDF (136 Kb, Info)

Abstract:

In the paper analogously to the notion of fuzzy numbers ([10, 11, 12, 13, 14, 18], the notion of the IFnumber is introduced, using a new approach and it is studied. Especially it is proved that the space of all IFnumbers with a convenient metric function is a complete metric space.

Keywords:

Intuitionistic fuzzy sets, Fuzzy numbers, Metric spaces.

AMS Classification:

03E72, 08A72.

References:

 Atanassov, K. (1999) Intuitionistic Fuzzy Sets: Theory and Applications. Studies in Fuzziness and Soft Computing. Physica Verlag, Heidelberg.
 Atanassov, K. (2012) On Intuitionistic Fuzzy Sets Theory. Springer, Berlin.
 Atanassov, K. (2007) Remark on intuitionistic fuzzy numbers. Notes on Intuitionistic Fuzzy Sets, 13(3), 29–32.
 Atanassov, K. T., Vassilev, P. M., & Tsvetkov, R. T. (2013) Intuitionistic Fuzzy Sets, Measures and Integrals. Prof. M. Drinov Academic Publishing House, Sofia.
 Ban, A. (2006) Intuitionistic Fuzzy Measures. Theory and Applications. Nova Sci. Publishers, New York.
 Ban, A., & Coroianu, L. (2011) Approximations of intuitionistic fuzzy numbers generated from approximations of fuzzy numbers. Recent Advances in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics, Vol. I: Foundations. Warsaw, SRI Polish Academy of Sciences, 43–61.
 Boccuto, A., Riečan, B., Vrábelová, & M. Kurzweil (2009) Henstock Integral in Riesz Spaces, Bentham.
 Burillo, P., Bustince, H. & Mohedano, V. (1994) Some definitions of intuitionistic fuzzy number. First properties. Proc. of the First Workshop on Fuzzy Based Expert Systems (D. Lakov, Ed.), Sofia, 28–30 Sept. 1994, 53–55.
 Ciungu, L., & Riečan, B. (2010) Representation theorem for probabilities on IFSevents. Information Sciences, 180, 703–708.
 Congxin, W., & Gong, Z. (2001) On Henstock integral of fuzzynumbervalued functions, Fuzzy Sets and Systems, 120(3), 523–532.
 Congxin, W., & Ming, M. (1991) On embeding problem of fuzzy number space: Part 1. Fuzzy Sets and Systems 44, 33–38.
 Goetchel, R., & Voxman,W. (1986) Elementary fuzzy calculus. Fuzzy Sets and Systems, 18, 31–43. 12
 GuangQuan, Z. (1991) Fuzzy continuous function and its properties. Fuzzy Sets and Systems, 43, 159–171.
 Ming, M. (1993) On embedding problem of fuzzy number space. Part 4. Fuzzy Sets and Systems, 58, 185–193.
 Riečan, B. (2012) Analysis of Fuzzy Logic Models. Intelligent Systems (V. M. Koleshko ed.), INTECH, 219–244.
 Riečan, B., & Mundici, D. (2002) Probability inMValgebras. Handbook of Measure Theory (E. Pap ed.), Elsevier, Heidelberg.
 Riečan, B., & Neubrunn, T. (1997) Integral, Measure, and Ordering. Kluwer, Dordrecht.
 Uzzal Afsan, B. M. (2016) On convergence theorems for fuzzy Henstock integrals. Iranian J. of Fuzzy Systems (in press).
 Zadeh, L. A. (1965) Fuzzy sets. Inform. and Control, 8, 338–358.
 Zadeh, L. A. (1968) Probability measures of fuzzy events. J. Mat. Anal. Apl., 23, 421–427.

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