With respect to multiple attribute decision making problems with interval-valued intuitionistic fuzzy information, some operational laws of interval-valued intuitionistic fuzzy numbers, score function and accuracy function of interval-valued intuitionistic fuzzy numbers are introduced. An optimization model based on the ideal solution and min-max operator, by which the attribute weights can be determined, is established. We utilize the interval-valued intuitionistic fuzzy weighted arithmetic

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... raging (IIWAA) operator to aggregate the interval-valued intuitionistic fuzzy information corresponding to each alternative, and then rank the alternatives and select the most desirable one(s) according to the score function and accuracy function. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.