An equivalent condition to the Jensen inequality for the generalized Sugeno integral

摘要

For the classical Jensen inequality of convex functions, i.e., H(1μ(D)∫Dfdμ)≤1μ(D)∫DH∘fdμ, an equivalent condition is proved in the framework of the generalized Sugeno integral. Also, the necessary and sufficient conditions for the validity of the discrete form of the Jensen inequality for the generalized Sugeno integral are given.