In several applications, in particular in multicriteria decision support, averaging operators play an important role. Based on several types of fuzzy integrals, we introduce a class of such operators in the intuitionistic fuzzy environment. We generalize several approaches known from the literature. We discuss some properties of this new operator and propose a new decision model for intuitionistic fuzzy environment. An illustrative example is also included.

In this paper, the well-known Egoroff's theorem in classical measure theory is established on monotone non-additive measure spaces. Taylor's theorem, which concerns almost everywhere convergence of measurable function sequence in classical measure theory, is also generalized. The converse problem of the theorems are discussed, and a necessary and sufficient condition for the Egoroff's theorem is obtained on semicontinuous fuzzy measure space with S-compactness.