The actual shade braket is mounted (riveted) to an angle bracket and painted. Your shade should have manufacturer logo on it somewhere. (It looks like a common pleated shade bracket, however each brand/model has it's own bracket)
Look up manufacturer online and give them a call, telling them that you need a ceiling mount bracket for their model xxxxx shade.
When it arrives, remove/drill out rivet and fasten new shade bracket to angle using as rivet as they did, or a small nut & bolt.
(Or you can tell me the make & model of your shade and I will get the info for you...)
Inquiring minds want to know...