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To solve the interval-valued intuitionistic fuzzy decision-making problems with high-dimension data, the fuzzy matrix is extended to the fuzzy tensor in this paper. Based on the constructed tensor definition, we propose the generalized interval-valued intuitionistic fuzzy weighted averaging (GIIFWA) and generalized interval-valued intuitionistic fuzzy weighted geometric (GIIFWG) operators. By exploring the properties of GIIFWA and GIIFWG operators, a new algorithm is presented to solve the interval-valued intuitionistic fuzzy multiple attribute group decision-making problem. Two typical application examples are also provided to demonstrate the efficiency and universal applicability of our proposed method.