Let's assume we would agree that all people under 1.70m are definitely not tall, and all people over 1.90m are definitely tall. Then we could draw the following "fuzzy" function G(x):

So we have solved the problem of the sharp border between "big" and "not big" by creating a smooth transition. 

The transition is not vertical, as with the "sharp" sets, but has a more or less pronounced gradient. The transition is linear (one line). We could also have taken any non-linear curve. Because of the complex calculation of non-linear transitions, in practice the fuzzy membership functions are modeled from lines.