1A:uti→Z≥ looks like a function definition to me but i'm not sure written as i've written it it is entirely correct. if u trust my limited mathematical knowledge u should use this to define the indicator function but then u don't need the whole function definition in your equation. i think you can say something like this.
$sim_2(u,c)=...\sum 1_{\bf A}$
where $1_{\bf A} : u_i^t \to {0,1}$
in words this says "the similarity measure between u and c equals the number of elements in $u^t$ (cardinality) that satisfy the function $1_{\bf A}$, where the function $1_{\bf A}$ takes an element of ut and returns a 0 or 1". i understand that's what your trying to say?
anyway, the important thing to make clear in your definition is that the indicator function maps a single element of ut (i.e. $u_i^t$) to {0,1}. i.e. given some element uti the indicator function returns either a 0 or 1 dependent on whether the element is in A. it is when this is summed over all N that we get a positive integer (i.e. $\sum 1_{\bf A} \to \mathbb{Z}^\geq$).
you could alternatively wrap the whole definition up like this: $sim_2 : u X c \to \mathbb{Z}^\geq$. this says, the function $sim_2$ takes 2 inputs (u and c) and returns a positive integer. and then include the full function definition: $sim_2(u,c)=\frac{1}{∣∣ct∣∣+∣∣ut∣∣}\sum 1_{\bf A}$
i think what i'm saying is correct. hope it helps. you might want a second opinion though. not from a doctor just a real mathematician.
good luck!