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http://ifigenia.org/wiki/issue:nifs/27/4/78-81
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| Title of paper:
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Note on one inequality and its application in intuitionistic fuzzy sets theory. Part 2
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| Author(s):
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 27 (2021), Number 4, pages 78-81
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| DOI:
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https://doi.org/10.7546/nifs.2021.27.4.78-81
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| Download:
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 PDF (136 Kb, File info)
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| Abstract:
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In the paper, the inequality [math]\displaystyle{ \frac{\mu^{\frac{1}{\nu}}}{\nu} + \frac{\nu^{\frac{1}{\mu}}}{\mu} \leq \frac{1}{2\mu\nu} - 1 }[/math] is introduced and proved. The same inequality is valid for [math]\displaystyle{ \mu = \mu_A(x), \nu = \nu_A(x) }[/math], where [math]\displaystyle{ \mu_A }[/math] and [math]\displaystyle{ \nu_A }[/math] are the membership and the non-membership functions of an arbitrary intuitionistic fuzzy set [math]\displaystyle{ A }[/math] over a fixed universe [math]\displaystyle{ E }[/math] and [math]\displaystyle{ x \in E }[/math].
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| Keywords:
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Inequality, Intuitionistic fuzzy set.
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| AMS Classification:
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03E72
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| References:
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- Atanassov, K. (1999). Intuitionistic Fuzzy Sets: Theory and Applications. Springer, Heidelberg.
- Atanassov, K. (2012). On Intuitionistic Fuzzy Sets Theory. Springer, Berlin.
- Vassilev-Missana, M. (2021). Note on one inequality and its application in intuitionistic fuzzy sets theory. Part 1. Notes on Intuitionistic Fuzzy Sets, 27(1), 53–59.
- Zadeh, L. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.
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