IJPAM: Volume 116, No. 2 (2017)

Title

GAUSS-WINKLER TYPE INEQUALITY
FOR SUGENO INTEGRALS

Authors

Dug Hun Hong
Department of Mathematics
Myongji University
Yongin Kyunggido, 449-728, SOUTH KOREA

Abstract

This paper propose a Gauss-Winkler type inequality for Sugeno integrals. Indeed, we find the optimal constant $H$ for which the following Gauss-Winkler type inequality for fuzzy integrals

\begin{displaymath}
\left((S)\int_0^1x^2 f(x)d\mu\right)^{2} \leq H\left((S)\int_0^1 f(x)d\mu\right) \left((S)\int_0^1x^4 f(x)d\mu \right)
\end{displaymath}

holds where $f:[0,1]\to [0, \infty)$ is a nondecreasing function and $\mu$ is the Lebesgue measure on $\mathbb{R}$. Some examples are provided to illustrate the validity of the proposed inequality.

History

Received: 2017-06-09
Revised: 2017-06-21
Published: October 7, 2017

AMS Classification, Key Words

AMS Subject Classification: 26E50
Key Words and Phrases: fuzzy measure, Sugeno integral, Gauss type inequality

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How to Cite?

DOI: 10.12732/ijpam.v116i2.19 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 116
Issue: 2
Pages: 479 - 487


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