Suppose, we have to variables:
A : value lies between (0-1)
B : value lies between (0-1)
For us, Lower value of A and higher value of B is favorable.
e.g:
A=0.3 and B = 0.7 -> GOOD
A=0.8 and B = 0.5 -> BAD
question is how to create a single measure mathematically : i.e combining value of A and B giving a score between (0-1) which will give us a measure of overall goodness ?
A+B -> 0.9 OVERALL GOOD
A+B -> 0.1 OVERALL BAD
What about the following score function.
$$1-\frac{|A|+|1-B|}{2}=1-\frac{A+1-B}{2}=\frac12+\frac{B-A}{2}$$
If $A$ is huge, the score should reduces.
If $B$ is small, the score is small as well.
Consider the worst case scenario, if $A=1$ and $B=0$, the score is $\frac12-\frac12=0$.
Consider the best case scenario , if $A=0$ and $B=1$, the score is $\frac12+\frac12=1$.