I want to construct a function that have these properties:
f( x, y) = f(y,x) f(-x,-y) = -f(x,y) f( 1,x) = 1 (if 1≥x>-1) f(-1,x) = -1 (if 1>x≥-1) f(1,-1) should be undefined f(x,-x) = 0 f(x,a) should be growing for all -1 < x < 1
And as suspected x, y should be in [-1,1].
I want to use it to create some sort of mean-like value, to use when I have two probabilities (ranging from certainly true (1) to unknown (0) to certainly false (-1)).
How do I construct this function?