I'm guessing I know which camp you are in when it comes to being either for or against fuzzy logic.
Fuzzy logic uses a set of if/then rules to provide hardware and software designs that are cheaper and more reliable than systems trying to approximate Nyquist equations, for example. You can also create a feedback loop to fine tune the rules.
Fuzzy logic control systems have been shown to be interchangable with classic control systems which use all the math you are referring too.
I applaud your passion but even Einstein recognized that mathematics when it comes to physics should always be recognized as a model and an approximation.
"As far as the laws of mathematics refer to reality, they are not certain, as far as they are certain, they do not refer to reality." -Albert Einstein
Your post smacks of a religious fervor that mathematics is certain when it refers to reality.
Your attitude is all too common in Western academia and hence Japan has had much better success in adopting and applying fuzzy logic than we have.
I think a better argument is to state that mathematical models are just that, models, and while you can blindly apply formulas (much as a computer), you'll miss out on the gaps, e.g assumptions, made along the way to make the model work.
The gap between Newtonian physics and quantam mechanics being the classic example.
Feynman had a similar attitude as yours with respect to the fact that Newtonian physics do not reflect reality at the quantam level, but quantam mechanics works for both the macro and quantam level and hence tried to teach quantam as an introductary physics.
Your argument is similar. Has the US adopted Feynman's philosophy of skipping Newtonian physics and starting with quantam?