Call for Papers for the 27th International Conference on Intuitionistic Fuzzy Sets is now open!
Conference: 5–6 July 2024, Burgas, Bulgaria • EXTENDED DEADLINE for submissions: 15 APRIL 2024.
Conference: 5–6 July 2024, Burgas, Bulgaria • EXTENDED DEADLINE for submissions: 15 APRIL 2024.
Issue:Note on one inequality and its application in intuitionistic fuzzy sets theory. Part 1: Difference between revisions
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| abstract = The inequality <math>\mu^{\frac{1}{\nu}} + \nu^{\frac{1}{\mu}} \leq 1</math> is introduced and proved, where <math>\mu</math> and <math>\nu</math> are real numbers, for which <math>\mu, \nu \in [0, 1]</math> and <math>\mu + \nu \leq 1</math>. The same inequality is valid for <math>\mu = \mu_A(x), \nu = \nu_A(x)</math>, where <math>\mu_A</math> and <math>\nu_A</math> are the membership and the non-membership functions of an arbitrary intuitionistic fuzzy set A over a fixed universe E and x | | abstract = The inequality <math>\mu^{\frac{1}{\nu}} + \nu^{\frac{1}{\mu}} \leq 1</math> is introduced and proved, where <math>\mu</math> and <math>\nu</math> are real numbers, for which <math>\mu, \nu \in [0, 1]</math> and <math>\mu + \nu \leq 1</math>. The same inequality is valid for <math>\mu = \mu_A(x), \nu = \nu_A(x)</math>, where <math>\mu_A</math> and <math>\nu_A</math> are the membership and the non-membership functions of an arbitrary intuitionistic fuzzy set <math>A</math> over a fixed universe <math>E</math> and <math>x \in E</math>. Also, a generalization of the above inequality for arbitrary <math>n \geq 2</math> is proposed and proved. | ||
| keywords = Inequality, Intuitionistic fuzzy sets. | | keywords = Inequality, Intuitionistic fuzzy sets. | ||
| ams = 03E72 | | ams = 03E72 |
Revision as of 23:48, 25 June 2021
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