I think you are mixing apples and oranges.
On the assumption that you mean ‘National Personal Trainer Institute’ with NPTI, then this is an organization through which to obtain a certification.
IHRSA is an organization for health and fitness clubs, and I have never heard that they have any stated preference for any given certifications. This is usually for the individual clubs to decide which one they recognize or not.
Here is a helpful link:
I Hope This Helps!