Fuzzy number-valued fuzzy measure and fuzzy number-valued fuzzy integral on the fuzzy set

In this paper, some new concepts — the fuzzy number-valued fuzzy measure, autocontinuity and null-additivity of fuzzy number-valued fuzzy measures on the fuzzy σ-algebra, and the fuzzy number-valued fuzzy integral on the fuzzy set — are introduced. Some properties of fuzzy number-valued fuzzy integrals and some convergence theorems for sequences of fuzzy number-valued fuzzy integrals on a fuzzy set are discussed.