Is it worth going for such precision with a fuzzy system in the first place?

I know that fuzzy is repeatable, I know how it works, and that it produces a set point based on rules which always give the same answer under the same conditions. (As opposed to a lay understanding which is that the output itself is fuzzy....)

But given that the whole fuzzy membership thing is, well, fuzzy, eg the slopes of the trapezoid ends and stuff like that, and the centroid approach to de-fuzzing, is it really of any value to get too anal about the precision of the setpoint and meeting it in the hardware?

We get to the point where we do anal maths on calculating membership levels and centroid positions (becasue that arithmetic is pretty trivial), losing sight of the fact that the membership definitions of stuff like cold, cool, warm, hot are loose in the first place.