Hi Yue, I believe the Type Definitions functionality is only available to Ariba customer support. I myself did not find that option under Core Administration and upon checking with Ariba, was informed that this is only available to Ariba support.
If you want to create a Partial catalog, you need to include TRUE under the "IsPartial" column in the CIF catalog template. Note that even when using a partial catalog, you will still need to specify information in the following three columns:
Supplier Part ID
SPSC Code / Classification Codes
Parametric Search Type is a functionality that allows you to search for catalog items using predefined custom search parameters. This involves the use of Type Definitions.