Abstract Intuitionistic fuzzy sets (IFSs) are successful to handle the uncertain situations of data. Distance measures of IFSs are important in the evaluation of IFSs relationships. In this paper, we analyzed the disadvantages of existing distance measures of IFSs and proposed a new distance measure called H-max of IFSs. We continued to point out some new results on intuitionistic t-norms and intuitionistic t-conorms and evaluated distance measure between two IFSs which are basically structured from these operations. Further, we combined the classification of t-representable intuitionistic fuzzy t-norms and t-conorms with the proposed distance measure to study some interesting properties. Moreover, we studied De Morgan triplets of IFSs based on the proposed distance measure. Finally, we applied the proposed distance measure to medical diagnosis problem examples and experimental validation on real-world datasets to check the applicability and effectiveness.