Normalization of an addition of two values

Question

I have the following expression which I want to normalize:

val = v1+ v2
v1: has real values >0
v2: has values between 0 and 1

I want to normalize val such that it gives values between 0 and 1.

Best regards,

Answer 1

Given your definition:

val = v1+ v2
v1: has real values >0
v2: has values between 0 and 1

we know that val is a real value $>0$. Mapping this onto a value between $0$ and $1$ simply requires a monotonic function that stays small as its input goes to infinity. A simple option might be $\text{val}_{\text{norm}} = 1-2^{-\text{val}}$

If you wanted more weight on v2 in the result you might consider normalizing v1 instead and then adding & scaling into the desired range.