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With respect to intuitionistic fuzzy multiple attribute decision making problems with preference information on alternatives, in which the information on attribute weights is completely unknown and the attribute values and preference information on alternatives take the form of intuitionistic fuzzy numbers, score function and accuracy function of intuitionistic fuzzy numbers, a new decision making analysis method based the minimum deviation is proposed. First, some operational laws of intuitionistic fuzzy numbers, score function and accuracy function of intuitionistic fuzzy numbers are introduced Then, to reflect the decision makerpsilas preference information, an optimization model based on the minimum deviation method, by which the attribute weights can be determined, is established. We utilize the intuitionistic fuzzy weighted averaging (IFWA) operator to aggregate the 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. The method can sufficiently utilize the objective information, and meet decision makerspsila subjective preference, can also be easily performed on computer. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.