Intuitionistic fuzzy similarity relations cause the similarity degree between objects in the intuitionistic fuzzy set too concentrated or the dissimilarity degree too high， leading to nreasonable classification results， and when constructing intuitionistic fuzzy similarity relation， the similarity degree and dissimilarity degree between objects are vulnerable to unimportant attributes. Therefore， a three-way decision model based on intuitionistic fuzzy similarity relation is proposed according to the intuitionistic fuzzy sets and the possibility theory. Firstly， the definitions of possibility measure and necessity measure are given. Combining with the Hausdorff measure， a distance formula is constructed and its properties are proved. The similarity degree and dissimilarity degree between objects in intuitionistic fuzzy sets are defined， and a new intuitionistic fuzzy similarity relationship is constructed.Then，the （λ₁，λ₂）-cut set under intuitionistic fuzzy similarity relation and the similar class under intuitionistic fuzzy （λ₁，λ₂）-cut set are defined， and the positive， negative and boundary fields of target set are further obtained. Finally， the rationality and effectiveness of the proposed model are verified through UCI data sets and examples.