In this paper, we have shown that the Moment type inequality has not satisfied for fuzzy integrals and it has proved with a stronger condition for fuzzy form. Also we have generalized D. H. Hong’s work [12], that was weaker version of Gauss’s inequality for Sugeno integrals. More presisly, he proved the inequality x2 ∫ ∞ x f(t)dμ ≤ ∫ ∞ 0 t2f(t)dμ, holds for all x ≥ c, where f(c) = 1 c , for c > 0 and f(t), t2f(t) are non-increasing functions on [0,∞) and μ is the Lebegue measure on R. In our generalization, we added an extra condition in Theorem 3.7. In this theorem, taking p = 0 and q = 2, we obtained Gauss type inequality for Sugeno integrals.
