Intuitionistic fuzzy similarity measures based on Frank t-norms family

•Extending a set of crisp similarity measures to the case of intuitionistic fuzzy sets.•The results are based on two cardinality measures.•The performance of these new similarity measures is verified using a set of numerical examples.

Intuitionistic fuzzy sets, proposed by Atanassov, have gained attention of many researches for applications in various fields. Different types of similarity measures for intuitionistic fuzzy sets were proposed and used in numerous applications. In this paper we extend some crisp cardinality measures to measures for intuitionistic fuzzy sets; the main role in this process is played by the Frank t-norm family.