Abstract: The similarity of intuitionistic fuzzy sets is widely used in artificial intelligence fields such as pattern recognition. In order to solve the problem of similarity measurement of intuitionistic fuzzy sets on continuous domain of discourse and incorporate the similarity analysis of intuitionistic fuzzy sets into the framework of logical reasoning, the similarities on continuous domain of discourse with the help of logical operators are constructed, one is integration before aggregation, and the other is aggregation and then integration, which proves that they satisfy the four conditions of similarity. Furthermore, considering the difference in the weights of each attribute in practical application, a weighted intuitionistic logical similarity satisfying the normalization condition on the continuous domain of discourse is proposed, and it is proved that they satisfy the four conditions of similarity. Finally, the two proposed similarities are applied to the fields of pattern recognition and market forecasting, and the results are consistent with the intuition.