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A membership function in fuzzy logic represents the degree of truth of the statement " belongs to the subset of the set ". The set can be split into the subsets and in ordinary set theory either or . In fuzzy logic, the membership function represents the degree to which . For example, let be the set of ages of people. Three subsets of are , , and (young, middle-aged, and old). Take some who is 28 years old. It cannot be strictly said whether belongs to or or even perhaps . To use fuzzy logic, we might define by: "If the person's age is , the person is 100% middle-aged. If their age is or , the person is 50% middle-aged." This Demonstration plots the function used to define membership, which depends on the and ; the center is and the 0% member boundary is at .
Contributed by: Vladislav Glagolev (March 2014)
Open content licensed under CC BY-NC-SA
Wolfram Demonstrations Project
Published: March 28 2014