# Choice of fuzzification function

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.