I would like to know how to put the following ideas in to a more formal mathematical notation:
Traditional methods implement a direct functional relationship between input and output signals:
I'd like to insert mathematical notation that helps to formalize what I just said here
However, the new system implements an indirect relationship where the input signals are translated via rules into linguistic variables and weightings. These are then interpolated at the output according to the set of weights and other rules that seek to mimic the same functional relationship as the traditional method:
Again, I'd like to insert mathematical notation that helps to formalize of what I just said here
On a descriptive level I have a project that has elements similar to fuzzy logic*. I'm wondering how I could make a basic attempt at mathematically formalizing it.
(* the irony)
EDIT
Does this:
$f: X \mapsto Y$
..apply in both cases? Or just the first?