September 2014
Intermediate to advanced
632 pages
21h 5m
English
Content preview from Soft Computing and Its Applications, Volume One
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Fuzzy Sets, Fuzzy Operators, and Fuzzy Relations 149
In this section, we dene type-2 fuzzy sets and some important associated con-
cepts. We provide simple mathematically expression to represent type-2 fuzzy sets
[183].
Denition 2.45 A type-2 fuzzy set, denoted , is characterized by a type-2 member-
ship function where and that is,
(2.108)
in which 0 can also be expressed as
(2.109)
where denotes union over all admissible x and u. For discrete universes of dis-
course is replaced by .
In Denition 2.45, the rst restriction that is consistent with
the type-1 constraint that 0 , that is, when uncertainties disappear
a type-2 membership ...
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