Fuzzy Logic

The fuzzy logic is a generalization of classic sets theory.

In the classic sets theory, a element is in a set or not.

For example, the fruit's universe, the orange is in set of citric fruits, and the apple is not in that set.

But, if we analyze the people's universe and make 2 sets: rich people and poor people. If anyone has more than US$ 500,000.00, that's rich, if anyone has less than US$ 500,000.00, that's poor.

Thus, someone has US$10,000.00; US$30,000.00; US$50,000.00; US$70,000.00; US$100,000.00; US$120,000.00; US$180,000.00; US$210,000.00; US$220,000.00; US$300,000.00; US$450,000.00; US$480,000.00; US$492,000.00; US$497,000.00; US$499,800.00; US$499,930.00; US$499,981.00; US$499,996.00; US$499,999.20; US$499,999.98; that's a poor people. And other someone has US$1,000,000.00; US$980,000.00; US$840,000.00; US$770,000.00; US$680,000.00; US$610,000.00; US$590,000.00; US$540,000.00; US$510,000.00; US$508,000.00; US$502,000.00; US$501,000.00; US$500,100.00; US$500,010.00; US$500,001.00; US$500,000.10; that's a rich people.

But, let's think: if anyone has US$499,999.97 and other one has US$500,000.01 they have the same money, because US$0.04 is almost no money, but they aren't in same set.

The fuzzy logic add the pertinence concept for each element. So, all elements are in all sets, but each element has a specific pertinence in each set.

We can use fuzzy logic in any situation, solving it as a linguistic problem. If you need classify the cars in big or small, is possible do 2 fuzzy sets, if you need classify the cars in big, small and median, is possible do 3 fuzzy sets, and successively.

I did the following video of a application that I developed for A.I. class.



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