This article concerns the well known Steffenson ineqaulity for fuzzy integrals. The Steffenson inequality has many refinenments such as the Fourier transform inequality, Abel inequality, Gauss inequality and Moment ineqialities. Besides the mentioned refinements, there is an another refinement so called Godunova-Levin-Chebaevskaya (GLC) inequality. The main aim to choose the GLC inequality to be inevstigated is the absence of research works on the GLC inequality neither in its classic form nor its fuzzy version. In order to obtain the fuzzy GLC inequality, we will attempt in the first step to obtain the fuzzy Steffenson inequality and relying on it fuzzy version of the fuzzy GLC inequality will be concluded. Several numerical example are given to prove validity of the obtained theoretical GLC inequality in practice.
