Membership Function

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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
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"Membership Function"
http://demonstrations.wolfram.com/MembershipFunction/
Wolfram Demonstrations Project
Published: March 28 2014