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In this paper, an improved technique for order preference by similarity to an ideal solution (TOPSIS) method was proposed based on completely unknown attribute weight information, as well as taking multiple criteria decision making of interval-valued intuitionistic fuzzy number as the evaluation information. First of all, a cumulative interval score function considering the influence of hesitation as well as a cumulative score function containing the risk preference of the decision maker were constructed. Then, a new information entropy function was constructed by using the newly defined score function, which presents a new method that directly utilizes evaluation information to obtain criterion weight. Next, all schemes were sequenced by virtue of relative closeness and the criterion weight of each alternative and ideal scheme. Finally, the effectiveness of the proposed method was illustrated by comparison with examples.