could you help me, what benefit of using fuzzy set? why we need it?
what are its application?

 

Fuzzy sets allow a controller to interpret more vague, human-like terms into a control parameter and are used with fuzzy logic - the driving mechanism behind a fuzzy logic controller. It allows a fuzzy controller to determine just "how much" a value is true. Take an example of temperature.

If you say it is slightly cold, this has no meaning to a digital device. The fuzzy set allows the controller to determine what temperature corresponds to 'slightly cold' and interpret it as a combination of, say 0.5 cold and 0.5 warm - meaning the quantification of the cold is the middle of both cold and warm - having a membership of 0.5 warm and 0.5 cold ( it is half true in each case, making the membership in hot = 0).

From this, the controller can apply a set of rules to happen when conditions are met (e.g. If the temperature is cold, then turn off the fan, or If the temperature is warm, let the fan run at low speed). The values are evaluated for each rule and combined in some fashion using a defuzzifier.