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The concept of the Takagi-Sugeno Intuitionistic Fuzzy Systems (TS-IFSs), which is an extension of the TS Fuzzy System, is introduced. In this paper, we prove that the multi-input single-out TS-IFSs are universal approximators, which can give theoretical support to practically operation. The TS-IFSs designed in this paper use any types of continuous intuitionistic fuzzy sets, typical types of intuitionistic fuzzy logic, intuitionistic fuzzy rules with linear TS rule consequent and the generalized centroid defuzzifier. The paper first constructively prove that the TS-IFSs can uniformly approximate any multivariate polynomial with arbitrarily small error and then the TS-IFSs can uniformly approximate any multivariate continuous function with arbitrarily high approximation accuracy is proved.