Real-valued Choquet integrals with fuzzy-valued integrand

The Choquet integral of a real-valued function defined on a set of attributes with respect to a signed fuzzy measure is generalized for allowing a fuzzy-valued function to be its integrand while keeping its value to be a crisp real number. Thus, the Choquet integral can be used as a defuzzifying aggregation tool to deal with data set involving categorical attributes, linguistic variables, and/or fuzzy numbers. A numerical method with the relevant algorithm is developed to estimate the value of the Choquet integral for any given fuzzy-valued function.