# Membership Function

Membership Function

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 .

a

A

Ω

Ω

A,B,C,…

a∈A

a∉A

a∈A

Ω

Ω

Y

M

O

a

a

Y

M

O

M

x

x-s

x+s

x

s

x

x±2s