Calculation method of nonmonotonic interval-valued and fuzzy-valued Choquet integrals

A relative effective approach to calculate the Choquet integral of fuzzy-valued function with nonmonotonic fuzzy measure is proposed. Base on the connection between the Choquet integral value of the real-valued function and the Choquet integral values of its order-preserving functions, it is shown that the minimum and maximum of the integration of interval-valued function must be reached by ones of the critical cut point generated functions of the interval-valued integrand. With the MATLAB software, the efficiency and reliability of the proposed method in solving the nonmonotonic Choquet integral of fuzzy-valued function is demonstrated by the illustrative examples.