Alright, Peter...
I will buy into the idea that once the Fuzzy Rules are developed they become the "formulas".
HOWEVER... (rant alert!)
The point that I have always made, regarding PID (for these last 4 or 5 years), is that a programmer does NOT have control over how the response is generated, and ultimately, what the response is during the course of experiencing a particular situation.
The response is produced, strictly, according to the HARD-CODED PID Formulas. There is NOTHING that a programmer can do to modify how the PID Formulas respond.
Even if you change control-values, the response is still produced according to the formulas. The response is "hard-coded" in that sense. And, it is hard-coded in a manner beyond the programmers reach!
The advantage of Fuzzy is that the programmer can modify the response in any way he wants! Sure, it takes more code, but, as I have also said for the last 4 or 5 years, the onus is on the programmer to do whatever is necessary to get the proper response. That means, in the course of developing any process, the programmer needs to put in more effort, much more effort, than the operators or maintenance folks would have to just to overcome the short-comings of the programmer!
And, of course, one of the truely great things about software is, once you create a model, that model is available for all subsequent builds! If the model is developed to suit general-purpose needs then the model becomes a general-purpose solution.
One of the things that drives me nuts about the control-world is that too many programmers treat everything as if it was a "One-Off"! They think their particular problem is unique and has never been seen before.
There is far more duplicity in code than not!
I would (and do) dare say that control-responses end up being one of five cases: Turn it ON, Turn it OFF, Increase it, Decrease it, or do nothing.
Yeah, this went off on a bit of a wild-hair... tangents, don't cha luv 'em?