Issue:Note on one inequality and its application in intuitionistic fuzzy sets theory. Part 2

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Title of paper: Note on one inequality and its application in intuitionistic fuzzy sets theory. Part 2 Author(s): Mladen Vassilev-Missana 5 Victor Hugo Str., Sofia, Bulgaria statiamath@abv.bg Published in: Notes on Intuitionistic Fuzzy Sets, Volume 27 (2021), Number 4, pages 78-81 DOI: https://doi.org/10.7546/nifs.2021.27.4.78-81 Download:  PDF (136  Kb, Info) Abstract: 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]. Keywords: Inequality, Intuitionistic fuzzy set. AMS Classification: 03E72 References: 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. 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.