Set-builder Notation - define score on set whose elements are associated with another set

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this is probably straight forward, but I'm not sure how to deal with it. I'm looking for a mathematical representation.

In principle, I dealing with a set, let's call it F that contains elements (which are strings) that are used to calculate the set of values (lets say its length) in C. Now I want to define a function on F that in principle uses the elements of C.

Something like this:

$\text{score}(F) = C_k \cdot \max\ C_k\ \forall k \in C\ \text{where } C_k = \text{length of} F_k$

What is the best way to describe this mathematically? Thanks