A fuzzy Choquet integral with an interval type-2 fuzzy number-valued integrand

Fuzzy integrals have been used to fuse the evidence or opinions from a variety of sources. These integrals are nonlinear combinations of the support functions and the (possibly subjective) worth of subsets of the sources of information, realized by a fuzzy measure. There have been many applications and extensions of fuzzy integrals and this paper proposes a fuzzy Choquet integral, where the integrand takes an interval type-2 fuzzy number and the fuzzy measure is real number-valued. Interval type-2 fuzzy numbers encode the second-order uncertainty in a fuzzy number. Type-2 fuzzy numbers have been been shown to be useful in many applications, including computing with words and control systems. We illustrate our method on several numerical examples as well as on a bioinformatics application.