User View Permissions

I'm wondering if it's possible to set up view permissions in my projects table based on a user's preference in the contacts table. For example, we have project type 1,2,3 and 4. User 1 only wants to see project types 1 and 2 and selects that in a multi-select text field in the contacts table on their record. 

Is there a way to set the view permissions for that role in the projects table so User 1 only sees projects where Project type equals his selections in the multi-select text field?

Thanks!

------------------------------
Nathan Allan
------------------------------