Abstract
Two types of vector-valued Choquet integral models are proposed. Vector-valued Choquet integral models are vector valued functions calculated by m times Choquet integral calculations with respect to the m-th fuzzy measure vector. This model is an extension of the product of a matrix and a vector. Logical vector-valued Choquet integral models are extend to functions for which the input and output vectors are vectors with coefficients in the interval [0, 1] and fuzzy measures are set functions that map the interval [0, 1]. If the sum values of the set function values are equal to 1 for all subsets of the domain of the fuzzy measures, then the sum of the output values is 1. To introduce the symmetric difference expressions, some non-monotone fuzzy measures can be transformed to monotone fuzzy measures and can be interpreted on the basis of Shapley values etc.
