Fuzzy Logic
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FUZZY LOGICM Rizwan Aqeel
MSCS 3
UIIT Arid Agriculture University
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CLASSICAL SETS A classical set is a container that wholly
includes or wholly excludes some element
Allow !ull Mem"ershi# or $o Mem"er shi#
Mem"er shi# de%ined "y Characteristic%unction
Characteristic %unction& 'A(x) where 'A(x) *+ i%
x,A and 'A(x) *- i% x,A
.xam#les &/ays o% 0ee1 * 2MondaySunday4
MSCS3 Students*2rizwan5 zu"air4
6ive /inosaurs * 2em#ty4
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FUZZY SETS .xtension o% Classical Set
Allow #artial mem"ershi#
/o not restrict themselves to something lying
wholly in either set A or not in set A .xam#le 7eight
Short 7eight * 2+5853595:4
Medium 7eight * 2959:5:5::5;4
Tall 7eight * 2:5::5;5;:5<5<:4
; !eet heighted o"=ect >
More Mem"er shi# in Medium and less in Tall
height set
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FUZZY SETS 7ow we de%ine old> Is 9- year old house is
old> I% yes then what a"out 3? year ++ month
old house>
0e can not de%ine a clear cut "oundaries
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FUZZY SETS
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FUZZY SETS
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FUZZY SETS
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LINGUISTIC VARIABLES Ta1es words or sentences as values
Set o% values that it can ta1e is called a term
set
.ach value in the term is a %uzzy varia"lede%ined over a "ase varia"le
6inguistic varia"le @ !uzzy varia"le @ "ase
varia"le
.xam#le& Age 5 terms o% this linguisticvaria"le5 which are %uzzy sets could "e
Bold5 Byoung 5 Bvery old
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FUZZY LOGIC !uzzy 6ogic is a su#er set o% conventional
(Doolean logic) that has "een extended to
handle the conce#t o% #artial truthEtruth
values "etween com#letely true andcom#letely %alse
In %uzzy logic a #ro#osition may "e true or
%alse or have any intermediate truth value
such as may "e true Truth o% any statement "ecomes the matter
o% degree
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MEMBERSHIP FUNCTION(Μ) Calculate degree o% truth
Truth values ranges "etween -- to +-
Consider& Asad is old
0e de%ine 'Fld %unction o#erating on the%uzzy set o% old #eo#le !unction ta1es as
in#ut one varia"le5 which is age and returns
a value "etween -- and +-
I% age * <: 'Fld( age )* <: Good Mem"ershi#
I% age * 8- 'Fld( age ) * 8+0ea1
Mem"ershi#
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FUZZY VS PROBABILITY Doth o#erate on the same range H-- to +-
.xam#le & Am"er is a 8- year old girl
'Fld(Am"er) * -8
In #ro"a"ility& There is 8-J chance thatam"er "elongs to the set o% old #eo#le5 there
is an K-J chance that she does not "elong to
the old #eo#le
In %uzzy terminology it means amna has 8-Jmem"er shi# in the old set There is no
chance involved $o guess wor1 le%t %or
system to classi%y am"er as old or young
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LOGICAL AND FUZZY
OPERATORS
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FUZZY SET REPRESENTATION Tall * (-L:5 -8:L::5 KL;5 +L;:5 +L<)
$umerator & Mem"ershi# value
/enominator& Actual value o% the varia"le
!or instance the %irst element -L: is meaningthat a height o% : %eet has - mem"ershi# in
the set o% all #eo#le5 li1ewise men who are
;: or < %eet or < %eet tall have a
mem"ershi# value o% maximum +
!uzzy Set
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FUZZY RULES I% x is A then y is D
I% hotel service is good then ti# is average
x and y are varia"les and A5 Good5 Average5 D
are some distri"utionsL%uzzy sets Two arts Antecedent and Consequent
7ow is consequent a%%ected "y the antecedent>
The consequent s#eci%y that a %uzzy set "e
assigned to the out#ut The im#licaiton %unctionthen modi%ies that %uzzy set to the degree
s#eci%ied "y the antecedent The most common
ways to modi%y the out#ut %uzzy set are
truncation using the min %unction
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FUZZY INFERENCE SYSTEM !ive #arts o% !uzzy in%erence #rocess
!uzzi%ication o% the in#ut varia"les
A##lication o% %uzzy o#erator in the
antecedent Im#lication %rom antecedent to consequent
Aggregation o% consequents across the rules
/e%uzzi%ication o% out#ut
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FUZZY INPUTS
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APPLY FUZZY OPERATOR
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APPLY IMPLICATION METHOD
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AGGREGATE ALL OUTPUTS
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DEFUZZIFY
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MATLAB DEMO
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THANK YOU