An extended Chebyshev type inequality for the Sugeno integral on abstract spaces is studied. More precisely, necessary and sufficient conditions under which the inequality ∫ A φ(f * g) dμ ≥ (∫ A φ(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. © 2010 IEEE.