Surely a set cannot undergo a change ( due to the extensionality principle).
But in some contexts, we would like to think of something like this.
For example, in linguistics, one approach to define the meaning ( more precisely the extension ) of a word ( an noun or an adjective) is to say that a word refers to a set. So it will be said that " man " means ( refers to) M = { x| x is an animal endowed with rationality} ( assuming the old aristotelian definition of man as animal rationale).
This approach allows linguits ( in semantics) to explain the meaning of sentences in terms of membership relation or of inclusion relation, that is to define the meaning of a sentence in terms of precise " truth conditions". " Peter is human " <--> " Peter is a member of the set M ".
The problem is that (1) we do not believe that the meaning of " man" changes over time but that (2) there is no " constant" set such as the one I have just defined ( due to the fact that some men die and some new ones are born).
So, it would be interesting to be able to say that our set of humans " changes". Are there theoretical means to say this precisely?
Are there other contexts than linguistics in which this need for " changing sets" could be felt?