The drawbacks of the existing continuous interval-valued intuitionistic fuzzy ordered weighted average(C-IVIFOWA) operator are illustrated by an example, and the standard negation is introduced to develop the dual continuous ordered weighted average(DC-OWA) operator. Then, the improved continuous interval-valued intuitionistic fuzzy ordered weighted average(IC-IVIFOWA) operator is proposed to overcome the shortages. Based on the IC-IVIFOWA operator, the improved weighted continuous interval-valued intuitionistic fuzzy ordered weighted average(WIC-IVIFOWA) operator is defined to the aggregation of multiple interval-valued intuitionistic fuzzy numbers. Some desirable properties of this operator are proofed. An interval-valued intuitionistic fuzzy multiple attribute decision making approach is proposed by using the WIC-IVIFOWA operator, and a practical example is given to illustrate the effectiveness of the proposed approach.