M. R. Karimzadeh - Department of Mathematics, University of Maragheh, Maragheh, Iran
B. Daraby - Department of Mathematics, University of Maragheh, Maragheh, Iran
A. Rahimi - Department of Mathematics, University of Maragheh, Maragheh, Iran

In this paper, we have proved Diaz-Metcalf inequality for fuzzy integrals. More precisely:\\If f, g: [۰, ۱]\to\mathbb{R} are continuous and strictly increasing functions, then the fuzzy integral inequality - \hspace{-۱em} \int_۰^۱ f^s d\mu\cdot  - \hspace{-۱em} \int_۰^۱  g^sd\mu\le  - \hspace{-۱em} \int_۰^۱\left(f\cdot g\right)^sd\mu,holds, where s>۱ and \mu is  the Lebesgue measure on \mathbb{R}. In addition, we have shown this inequality for pseudo-integrals.

Diaz-Metcalf type inequality, Fuzzy integral, integral inequality, pseudo integral