No. Permissions are project level configuration.
However, they do have some flexibility and you can do something like this. For example...
If you use issue-level security, it's quite easy to set up post-functions to automatically set security (and beacuse you want to do it by issue type, you can have "set security level A" in one workflow for type A and "sec level B" for type B and so-on)
You can play tricks with users or group custom fields
You might consider the use of current-reporter-browse permission which isn't about issue types, but locks users out of issues they didn't raise.
and and and
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