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http://ifigenia.org/wiki/issue:nifs/27/1/53-59
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| Title of paper:
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Note on one inequality and its application in intuitionistic fuzzy sets theory. Part 1
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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 1, pages 53–59
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| DOI:
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https://doi.org/10.7546/nifs.2021.27.1.53-59
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| Download:
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 PDF (199 Kb, Info)
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| Abstract:
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The inequality [math]\displaystyle{ \mu^{\frac{1}{\nu}} + \nu^{\frac{1}{\mu}} \leq 1/2 }[/math] is introduced and proved, where [math]\displaystyle{ \mu }[/math] and [math]\displaystyle{ \nu }[/math] are real numbers, for which [math]\displaystyle{ \mu, \nu \in [0, 1] }[/math] and [math]\displaystyle{ \mu + \nu \leq 1 }[/math]. 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]. Also, a generalization of the above inequality for arbitrary [math]\displaystyle{ n \geq 2 }[/math] is proposed and proved.
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| Keywords:
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Inequality, Intuitionistic fuzzy sets.
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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.
- Fikhtengolts, G. (1965). The Fundamentals of Mathematical Analysis. Vol. 2, Elsevier.
- Zadeh, L. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.
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