Fuzzy Logic

7/18/2019 Fuzzy Logic

http://slidepdf.com/reader/full/fuzzy-logic-5691777939061 1/22

FUZZY LOGICM Rizwan Aqeel

MSCS 3

UIIT Arid Agriculture University



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



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



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



FUZZY SETS



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



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



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#



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



LOGICAL AND FUZZY

OPERATORS



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



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



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



FUZZY INPUTS



APPLY FUZZY OPERATOR



APPLY IMPLICATION METHOD



AGGREGATE ALL OUTPUTS



DEFUZZIFY



MATLAB DEMO



THANK YOU

Fuzzy Logic

Documents

Transcript of Fuzzy Logic