How do membership symbols and fuzzy sets change the idea of belonging?

"Another symbol we’ll use a lot is “ ∈ ”, which means “is a member of.” Since Lizzy is a female, we can write: Lizzy ∈ F to show that Lizzy is a member of the F set. Conversely, we write: T.J. / ∈ F to show that T.J. is not. As an aside, I mentioned that every item is either in, or not in, a set: there are no shades of gray. Interestingly, researchers have developed another body of mathematics called (I kid you not) “fuzzy set theory.” Fuzzy sets change this membership assumption: items can indeed be “partially in” a set. One could declare, for instance, that Dad is “10% female,” which means he’s only 10% in the F set. That might or might not make sense for gender, but you can imagine that if we defined a set T of “the tall people,” such a notion might be useful. At any rate, this example illustrates a larger principle which is important to understand: in math, things are the way they are simply because we’ve decided it’s useful to think of them that way. If we decide there’s a different useful way to think about them, we can define new assumptions and proceed according to new rules. It doesn’t make any sense to say “sets are (or aren’t) really fuzzy”: because there is no “really.” All mathematics proceeds from whatever mathematicians have decided is useful to define, and any of it can be changed at any time if we see fit."