(T) fuzzy integral of multi-dimensional function

Firstly, based on the T fuzzy measure and (T) fuzzy integral of one-dimensional function, this paper defines multi-dimensional simple function using generalized T-norm and S - norm and obtains a theorem on the representation form of a common multi-dimensional measurable function. Then it introduces two operational symbols T and S, presents the definitions of T fuzzy integrals for the multi-dimensional simple function and a common multi-dimensional measurable function and discusses some properties which are similar to one-dimensional case.