I'm a relative newbie to fuzzie logic systems but I have some knowledge in mathematics. I have the following problem:

I want to fuzzify certain values. Some are in the range [-$\inf$,$\inf$] and some are in the range [$0$,$\inf$]. For the first range I have chosen the sigmoid function:

$f(x) = \frac{1}{1+e^{-x}}$

The question is, which fuzzification process I should use for the second range. Since the function $f(x) = \ln(x)$ transforms [$0$,$\inf$] to [-$\inf$,$\inf$] a natural choice could be:

$f(x) = \frac{1}{1+e^{-\ln(x)}} = \frac{x}{x+1}$

A different function could also be:

$f(x) = 1 - 2^{-x}$

Which one would be more suitable? Particularly when considering that I may want to compare values from both ranges.


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