In this work, we prove a Prékopa-Leindler type inequality for the Sugeno integral. More precisely, if 0 < λ 1 and h ((1 - λ)x + λy) ≥ f(x)1-λ g(y)λ, ∀ x, y ∈ ℝn, where h, f and g are nonnegative μ-measurable functions on ℝn, then fℝn hdμ ≥ (f ℝn fdμ) ∧ (fℝn gdμ), for any concave fuzzy measure μ. Also, we derive a general Brunn-Minkowski inequality (standard form) for any homogeneous quasiconcave fuzzy measure μ on ℝn. © World Scientific Publishing Company.