I think I can guess why you said this, this way, here goes: new people to fuzzy theory think of fuzzy sets in terms of probabilities or compare it with it. Since “normalized” in probability theory basically means adding up to 1, you stick with their terminology. I’d just like to point out that according to many fuzzy set texts such as Klir and Yuan, Ngyuen and Walker, Buckley and Eslami, and Zadeh’s paper use “normalized” to mean that sup{F}=1 (or max{F} when F is finite), where F indicates our fuzzy set. So, many fuzzy set theorists would call your sets short, medium, and tall “normalized.” I’d suggest that you edit this any say something “normalized in the sense of probability theory” or something similar.

Nice essay.