how to create a quality measure for this equation?

31 Views Asked by At

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
1

There are 1 best solutions below

0
On BEST ANSWER

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 $\frac12+\frac12=1$.