# Class of functions to combine several parameters into some "satisfaction index"

I'm sure the title itself is puzzling. But my problem is quite simple: I'm looking for a class of functions, that can combine several variables(all of them are within known ranges), given their values as input the function varies its output from 0 to 1 depending on how close these variables are to their maximums/minimums.

Hope this example will clarify what i'm trying to do:

• MinDamageSize is between 0 and 1, and its preferable value is 0
• MaxCashCompensation is between 1000 and 2000, and, as the name suggests, 2000 is preferable.
• MonthlyPayment is between 350 and 600 and 350 is preferable.

So i'm looking for a function F(MinDamageSize, MaxCashCompensation, MonthlyPayment) with following conditions on the ends:

• F(1,1000,600) = 0
• F(0,2000,350) = 1

And this function must have some interesting shape which is hard to guess. It represents market demand in insurance company game simulator.

I know i can use function that sums distances of variables from their desired values, but in my opinion it is too simple.

Can anyone suggest what class of functions i should use? Thanks in advance

Thus at the end of this imporovement your score would be $f(d_1,d_2,d_3)\mapsto f(w_1d_1,w_2d_2,w_3d_3)$, I hope the fact that f,d,w are the metric,the data,weight respectively is obvious.