Individual Custom Post Type Category/Tag Archives

I have created several Custom Post Types and can display them as intended, but when using the standard the_category() and the_tags() functions to display their respective Categories and Tags, the link generated is to a generic Category and Tag archive for all post types (which 404’d at first as well, but I was able to “fix” that with the information found here).

Is it possible to have a unique Category and Tag archive for each custom post type?

Example: I have a custom post type named “Perspectives” so ideally I would be able to link to http://mywebsite.com/perspectives/category/technology instead of http://mywebsite.com/category/technology.