Complex objects are often described by several attributes of arbitrary types. To calculate the similarity between complex objects, we propose the CoSim process, which provides a composed similarity function. CoSim applies existing similarity functions for each data type of the object. To calculate the overall similarity, we weight these type-specific similarities. We demonstrate the practical application of our approach by using a simple example of objects. The example involves numerical and categorical attributes. However, our presented idea is applicable to objects with attributes of arbitrary types.