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

Abstract—Fuzzy integrals have been used to fuse the evidence or opinions from a variety of sources. These integrals are non-linear 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 com-puting with words and control systems. We illustrate our method on several numerical examples as well as on a bioinformatics application. I.