A note on Jensen type inequality for Choquet integrals

The purpose of this paper is to prove a Jensen type inequality for Choquet integrals with respect to a non-additive measure which was introduced by Choquet[1] and Sugeno[20]; φ((C) ? fdμ) ≤ (C) ? φ(f)dμ, where f is Choquet integrable, φ [0,∞) is convex, φ(α) ≤ α for all α ∈ [0, ∞) and μ f (α)≤μ φ(f) (α) for all α ∈ [0, ∞). Furthermore, we give some examples assuring both satisfaction and dissatisfaction of Jensen type inequality for the Choquet integral.

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