Introduction to fuzzy logic

What does fuzzy logic means?

Simply, fuzzy logic is a method for processing ambiguous variables which can't be described precisely with numbers, such as height (i.e: is that man tall or short?), slow, noisy, etc. In fuzzy logic, this variables represented as a set which its elements are crisp values and satisfy a function. We call this function as membership function.

On the other hand, how does fuzzy logic works?


It works on 3 steps. first, Fuzzification, which describes all variables and its constraints as well. For example, if we look at a 10-years-old kid, we can say that he is young. Meanwhile, when we look at a 60-year-old grandpa, we can't say that he is young, we will say that he is old. But how about a 30 year-old man, can we say that he is old? or can we say that he is young?. This age is ambiguous, whether the man is young or old. So we need this fuzzification step to define which age is a "member" of young, ambiguous and old.

Second, Reasoning. This step introduced by Takagi-Sugeno, a k a Sugeno method. The idea of this method is to have a "linguistic" output value for given input. In this step, we will define "rules" that usually comes from experts. For example, IF the day is sunny AND the mood is good THEN lets hang out. but IF the day is rainy AND the mood is bad THEN lets take a nap (i hope this is not a bad example). got it?

Third, Defuzzification. This step works after we have all the given input and have all the rules defined. Instead of just getting linguistic output(s), defuzzification gives us an exact number on desired output. For example: the risk for this business is 62.34%, the man is 76% tall, the weather is 89.6% hot, etc