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Membership Function

​
100% member value
50
50% member boundary
30
center: 50
half: 30 and 70
max: 90
min: 10
A membership function in fuzzy logic represents the degree of truth of the statement "
a
belongs to the subset
A
of the set
Ω
". The set
Ω
can be split into the subsets
A,B,C,…
and in ordinary set theory either
a∈A
or
a∉A
. In fuzzy logic, the membership function represents the degree to which
a∈A
. For example, let
Ω
be the set of ages of people. Three subsets of
Ω
are
Y
,
M
, and
O
(young, middle-aged, and old). Take some
a
who is 28 years old. It cannot be strictly said whether
a
belongs to
Y
or
M
or even perhaps
O
. To use fuzzy logic, we might define
M
by: "If the person's age is
x
, the person is 100% middle-aged. If their age is
x-s
or
x+s
, the person is 50% middle-aged." This Demonstration plots the function used to define membership, which depends on the
x
and
s
; the center is
x
and the 0% member boundary is at
x±2s
.
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