<abstract><p>As we all know, when describing knowledge measures in the context of intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets, it is always considered as dual measures of entropy. However, information content and information clarity is closely related with the amount of knowledge. Motivated by this fact, in this study, we focus on a new axiomatic definition of knowledge measures for intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets. First, we present the formulas of the knowledge measures using different abstract functions, and we proved these functions satisfy the axioms. On the basis of mathematical analysis and numerical examples, we further analyze the characteristics of the suggested knowledge measure. Finally, in order to demonstrate how rational and useful the system we developed is, we provide medical diagnoses and specific multi-attribute decision problems.</p></abstract>