The information measure of interval-valued intuitionistic fuzzy sets holds extensive application value in decision-making and pattern recognition. The primary contribution of this paper lied in presenting a functional model for assessing the information content of interval-valued intuitionistic fuzzy sets. Initially, we introduced the concept of closest crisp set associated with interval-valued intuitionistic fuzzy set and explored its pertinent properties. Subsequently, taking into account the distance between interval-valued intuitionistic fuzzy set and its closest crisp set, we derived a comprehensive expression for functions pertaining to similarity measures, knowledge measures and entropy on interval-valued intuitionistic fuzzy set that adhered to specific criteria. Furthermore, we explored the interconversion between these three measures. The advantage of these functional expressions and transformation relationships lied in their ability to generate numerous formulas for defining information measures. Finally, we demonstrated the practical application of knowledge measure in investment case. The practicality of the proposed measures were corroborated through sensitivity analysis and comparative analysis.