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Diaz-Metcalf type inequality for Sugeno and pseudo-integrals | ||
| Iranian Journal of Fuzzy Systems | ||
| دوره 20، شماره 3، مرداد و شهریور 2023، صفحه 31-41 اصل مقاله (169.44 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2023.7637 | ||
| نویسندگان | ||
| M. R. Karimzadeh؛ B. Daraby* ؛ A. Rahimi | ||
| Department of Mathematics, University of Maragheh, Maragheh, Iran | ||
| چکیده | ||
| In this paper, we have proved Diaz-Metcalf inequality for fuzzy integrals. More precisely: \\ If $f, g: [0, 1]\to\mathbb{R}$ are continuous and strictly increasing functions, then the fuzzy integral inequality $$ - \hspace{-1em} \int_0^1 f^s d\mu\cdot - \hspace{-1em} \int_0^1 g^sd\mu\le - \hspace{-1em} \int_0^1\left(f\cdot g\right)^sd\mu,$$ holds, where $s>1$ and $\mu$ is the Lebesgue measure on $\mathbb{R}$. In addition, we have shown this inequality for pseudo-integrals. | ||
| کلیدواژه‌ها | ||
| Diaz-Metcalf type inequality؛ fuzzy integral؛ integral inequality؛ pseudo integral | ||
| مراجع | ||
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