Membership function

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membership function

A membership function maps items in a set to numbers in the real interval [0, 1].  This can be a one-to-one mapping where one item is a member of one and only one other set, or it could be a fuzzy and/or probabilistic relationship.  Membership functions are often used in fuzzy logic. For example, if one were to map hail into the set "large hail" versus "small hail," it is hard to define a specific cutoff (although the Storm Prediction Center has a definition for severe).  Instead, one could make a mapping that could indicate to what degree a hail sample belongs to the "large hail" set versus the "small hail" set. In approaches outside of fuzzy logic, these memberships could be viewed as a probabilistic relationship, where the number indicates the probability of belonging to that set.

Term edited 15 November 2021.

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