Membership function of a fuzzy set

Main characteristics of a fuzzy set is its membership function. There are many ways to represent membership function. Some of them are triangular shape, trapezoidal shape or Gaussian shape.

Membership functions

Membership function is usualy called m(x).

The interval for a single value of m is called a cut of a fuzzy set where alfa=m(x).


Alfa cut where alfa =0.5

The largest a cut interval is called the 'base' or 'the support' of the fuzzy set, and it is usually for m=0. The smallest a cut interval (a single value in triangular membership functions) is called the 'most likely value'.

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