The convergence for a sequence of fuzzy integrals of fuzzy number-valued functions on the fuzzy set

Abstract In this paper, a new concept of fuzzy number-valued fuzzy integral of fuzzy number-valued function with respect to fuzzy number-valued fuzzy measure on the fuzzy set is introduced, and some equivalent definitions of the above-mentioned concept are given, and its elementary properties are discussed, and a series of the convergent theorems of fuzzy number-valued fuzzy integrals on the fuzzy set are obtained.