Extended Chebyshev type inequality for Sugeno integral

An extended Chebyshev type inequality for the Sugeno integral on abstract spaces is studied. More precisely, necessary and sufficient conditions under which the inequality, ∫AΦ(f ⋆ g)dµ ≥ (∫AΦ(f)dµ) ⋆ (∫A Φ(g)dµ) or its reverse hold for an arbitrary fuzzy measure-based type Sugeno integral µ and a binary operation ⋆: [0, ∞)² → [0, ∞) and a nonnegative function Φ : [0, ∞) → [0, ∞), are given.