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http://ifigenia.org/wiki/issue:nifs/10/3/8-14
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| Title of paper:
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A note on the convergence of intuitionistic fuzzy sets
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| Author(s):
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| Presented at:
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8th International Conference on Intuitionistic Fuzzy Sets, Varna, 20-21 June 2004
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| Published in:
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"Notes on IFS", Volume 10 (2004) Number 3, pages 8—14
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| Download:
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 PDF (109 Kb, File info)
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| Abstract:
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In this paper is shown that fuzzy sets may be represented as a limit of an appropriate infinite sequence of intuitionistic fuzzy sets, depending on an operator [math]\displaystyle{ F_{\alpha,\beta} }[/math] introduced in [1]. The necessary and sufficient conditions for that are given. The situation looks like the one in the case of irrational and rational real numbers if we agree to make an analogy between proper intuitionistic fuzzy sets and rational numbers from one side, and between fuzzy sets and irrational numbers from the other side.
Also, for the first item, a necessary and sufficient conditions for the convergence of an infinite product and of infinite series are given, which are based on the notion of intuitionistic fuzzy set and on the operator [math]\displaystyle{ F_{\alpha,\beta} }[/math] only.
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| References:
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- K. Atanassov, Intuitionistic Fuzzy Sets. Springer Physica-Verlag, Heidelberg, 1999.
- A. Stamenov, A property of the extended intuitionistic fuzzy modal operator [math]\displaystyle{ F_{\alpha,\beta} }[/math], Proceedings of the Second Int. IEEE Conf. "Intelligent Systems", 22-24 June 2004, Varna, Bulgaria (in press).
- P. Vassilev, A note on the intuitionistic fuzzy set operator [math]\displaystyle{ F_{\alpha,\beta} }[/math], Proceedings of the Second Int. IEEE Conf. "Intelligent Systems", 22-24 June 2004, Varna, Bulgaria (in press).
- I. Privalov, Introduction in Theory of Complex Variable Functions. Maskow, Nauka, 1977 (in Russian).
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