We first define the quasi-addition and quasi-multiplication operations by introducing the inductive operator, and then, in the K-quasi-additive fuzzy measure space, we establish the K-quasi-additive fuzzy integral of a generally measurable set-valued mapping.Applying the integral transformation theorem, some basic properties of the K-quasi-additive fuzzy integrals with respect to this kind of setvalued mapping are studied. Finally, the generalized monotone convergence theorems of this kind of fuzzy integrals are obtained.