Steffensen type inequalities for fuzzy integrals

We provide several Steffensen type inequalities for the Sugeno integral. The inequalities are of the form - ? a b f g d µ ≤ A - ? a a + λ f d µ + B or - ? a b f g d µ ≤ A - ? b - λ b f d µ + B , where A, B are constants, µ is a fuzzy measure on R , g: a, b] ? 0, 1], f : a , b ] ? R + is nonincreasing or nondecreasing and λ = ( b - a ) ? - ? a b g d µ . We show that some of our sufficient conditions are also necessary.

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