Chances are if you've read any documentation on fuzzy logic, there will be nothing new in this essay. See the end of the essay for more information. The idea of fuzzy logic dates all the way back to Plato who proposed that there was a third region between true and false - the uncertain. It took many centuries before this system was ever formalized. In the 1900s a man called Lukasiewicz proposed a tri-valued logic system.
Membership functions can be incredibly simple, or incredibly complex.
The intersection and union operators are the obvious departure from both boolean logic and standard probabilty functions. To see why they are defined like this, let us look at an example. Hedges Hedges are operators that are independently created to modify the fuzzy values. Like a lot of fuzzy logic, they can be equated to English words. It has been done though, most notably by F.Wenstop who equated words to 7-valued fuzzy vectors.