In this paper we develop the similarity measure introduced by the Tversky contrast model and apply it on fuzzy sets using the cardinality of fuzzy sets and their operations. Based on this extended similarity definition we propose a new approach for comparing fuzzy objects and discuss some properties of the new similarity model. Some experimental examples are given to show the effectiveness of using this model against different cases. This work provides a method to compare objects with vague/fuzzy content and support further development of (fuzzy) data mining algorithms.