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-λg(y)λ, ∀ x,y ∈ ℝn, where h, f and g are nonnegative μ-measurable functions on ℝn, then [Formula: see text], 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.
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Román-Flores et al. (2007) studied this question.