Membership function (mathematics)

The membership function of a fuzzy set corresponds to the indicator function of classical sets. In fuzzy logic, it represents the Degree of truth. Degrees of truth are often confused with probabilities, although they are conceptually distinct, because fuzzy truth represents membership in vaguely defined sets, not likelihood of some event or condition.

For the universe X and given the membership-degree function

f : X→[0,1],

the fuzzy set A is defined as

A = {(x, f(x)) | x ∈ X}.

See also

• Defuzzification
• fuzzy set operations
• Rough set

External links

• Fuzzy Image Processing

See also: Membership function (mathematics), Defuzzification, Degree of truth, Fuzzy logic, Fuzzy set, Fuzzy set operations, Indicator function, Probability, Rough set, Set