As information resources have become more various and the number of the resources has increased, knowledge customization on the social web has been becoming more difficult. To reduce the burden, we offer a framework for context-based similarity calculation for knowledge customization using ontology on the CBR. Thereby, we newly developed context- and intensity-based similarity calculation methods which are applied to extraction of the most similar case considered semantic similarity and syntactic, and effective creation of the user-tailored knowledge using the selected case. The process is comprised of conversion of unstructured web information into cases, extraction of an appropriate case according to the user requirements, and customization of the knowledge using the selected case. In the experimental section, the effectiveness of the developed similarity methods are compared with other edge-counting similarity methods using two classes which are compared with each other. It shows that our framework leads higher similarity values for conceptually close classes compared with other methods.