In order to reflect the uncertainty of intervalvalued intuitionistic fuzzy set totally, three kinds of uncertain factors for intervalvalued intuitionistic fuzzy set are defined, namely, intuitionistic factor, fuzzy factor and span factor. Based on these three kinds of uncertain factors, a new type of intervalvalued intuitionistic crossfuzzy entropy for intervalvalued intuitionistic fuzzy set is given. Based on intervalvalued intuitionistic crossfuzzy entropy, a method to determine attribute weights is proposed. By using the weighted correlation coefficient between IvIFSs, a new algorithm for multiple attributes decisionmaking under intervalvalued intuitionistic fuzzy environment is given. Finally examples are used to analyze the feasibility and validity of the method.