fuzzy logic assignment 1

8/10/2019 Fuzzy Logic Assignment 1

1/21

MSc Intelligent Systems

Fuzzy LogicAssignment 1:Practical

Tutors: Prof. Francisco Chiclana Parrilla, r !enny Carter

Samuel "eays1#1#$%1&


2/21

Contents'ac(groun)............................................................................................................ $

In*ut +ariales.................................................................................................... &

-ame )elta...................................................................................................... &

A))ress )elta................................................................................................... &

-I -umer e)it )istance.................................................................................. &

ome *hone numer e)it )istance................................................................. /

0eogra*hical location...................................................................................... /

0en)er............................................................................................................ /

ut*ut +ariale................................................................................................... 2

3ules:.................................................................................................................. 2

efuzzi4cation.................................................................................................... 5

67*eriments an) T8ea(ing:................................................................................ 5

Conclusion........................................................................................................ 1%

'iliogra*hy......................................................................................................... 1%


3/21

'ac(groun)The aim of this re*ort is to *resent a fuzzy logic system 8hich enales one to

*ro)uce reasonale estimates of ho8 closely t8o a))resses match y )e4ning

rules that allo8 matching to ta(e *lace.

Master ata Management 9asel)en, $%%2 is a ty*e of soft8are solution that

has )e;elo*e) ra*i)ly an) has een in;este) in y many large cor*orate an)

go;ernment agencies. In essence it is a *rocess 8herey multi*le )ataase

sources < often from 8i)ely )i=erent systems such as C3Ms an) *ro)uct

catalogues < are ma**e) together to form one single ;ie8 of a customer or a

*ro)uct. This can either e a registry system 8here the master )ataase merely

*oints to recor)s it is mastering 9an) sen)s messages to inform them of the nee)

to u*)ate or change, an) *hysical 9or re*ository mo)els 8here an actual

)ataase mo)el is constructe) that is use) as the un)erlying )ataase mo)els

for all other systems after the outlying systems ha;e een *rocesse) in. 9>olter,

$%%? This can either e in the form of a single atch 4le 9initial loa) or )eltas8hich are )i=erence 4les et8een times 98hich is an es*ecially im*ortant use

case in registry style MM.

As an e7am*le of ho8 this 8or(s: there may e an in)i;i)ual calle) !ose*h

6thelert 'loggs. At a *articular an( he has a current account an) a loan. n

his current account he may e calle) !oe 6 'loggs. n his loan he is sim*ly

!ose*h 'loggs. The tas( of the system is to match such entries to inform the

an( they are one an) the same *eo*le. -aturally there are many more

)ata*oints that are ta(en into account 8hen matching. -ational insurance

numers for e7am*le may e *articularly rele;ant. -ames are often stan)ar)ise)

8ith the use of tales that ma* from common nic(names to their fullname.

Au7iliary tas(s inclu)e lin(ing househol)s of *eo*le 8ith the same a))ress an)

so forth. Most systems also ha;e a )egree of human interaction. So calle) )ata

ste8ar)s ta(e those entries 8hose matching is uncertain y the system an)

ma(e a )ecision. -aturally any match can full into three tiers: automatic

matching, re;ie8 matching an) no match.

The matching itself often in;ol;es ma(ing )ecisions aout 8ho or 8hat 8ill e

matche) together into one source. There are t8o main ty*es of matching engine,

one uses rules ase) system, as for e7am*le Informatica@s MM solution. 9Lira,

$%1 thers such as I'M@s initiate use *roailistic matching 8hich usually uses

the mutual information of )ata in the system that matches to conclu)e ho8

im*ortant the o;erla* is. 9>hei#!en Chen, $%1&, **. 12?#15/ My concern 8ill*rimarily e 8ith the rules matching, ecause this is 8here, to my min) there is

some o;erla*. ;iously this is a huge *roBect *otentially 8ith many research

*ossiilities. For this re*ort I 8ant to )emonstrate that some (in) of sim*le fuzzy

logic rule can e use) to match *otential )u*licates together 8ith )i=erent

)egrees of certainty ase) on 4;e )i=erent correlations et8een the )ata in t8o

entries < such as e)it )istance or numer of 4el)s for 9say a))ress that match.

-ote this is )i=erent to fuzzy string matching, 8hich is alrea)y use) in such

systems. Instea) it 8ill e necessary to create a rule set that )e4nes ho8 close@

t8o names are y ;irtue of their e)it )istances, among other things. The system

8ill largely consist of rules ase) on these ;arious metrics 8hich 8ill fee) to a

fuzzy set 8hich is a score of ho8 closely they are matche).


4/21

An interesting Duestion arises: is fuzzy logic necessaryE The (ey ene4t of fuzzy

logic is that it is *ossile to )e4ne uncertain conce*ts in a mathematical mo)el.

In this case, the linguistic ;ariale is close@ is y its ;ery nature uncertain.

67isting systems use com*le7 rule ases 8ith )etaile) rules aout e)it )istances

an) ;arious com*oun) con)itions. This therefore is an attem*t to see if a small

suset of that rules ase < the names < is re)ucile to a fuzzy system 8hosememershi* functions can e )e4ne) 8hich re*licates these rules. If they can,

then there is the *ossiility that these ;ery rules can e ca*ture) y some (in)

of Com*utation 8ith >or)s metho)ology. Instea) of a user s*ecifying that a

name must e 8ithin $ e)it )istance, say, the user coul) sim*ly state that the

t8o names shoul) e ;ery close@ 8ith an a**ro*riate relation eing forme) as a

conseDuence from the fuzzy system. This coul) *otentially s*ee) u* the time it

ta(es to )e;elo* the rules set.


5/21

In*ut +arialesI ha;e chosen 2 se*arate in*ut ;ariales:

-ame )elta

A))ress )elta

-I -umer e)it )istance

ome *hone numer e)it )istance

0eogra*hical location

0en)er

-ote the assum*tion is that in*uts ha;e alrea)y een stan)ar)ise), for e7am*les

nic(names to names. I trie) to stic( to the *rinci*le that 8here *ossile the total

memershi* gra)e shoul) eDual one so as not to *ro)uce strange results 8iththe out*ut function 8here *arameters are nee)lessly truncate) 9Lilly, $%1%, **.

1/#12. o8e;er, for the out*ut function itself this rule ha) to e ro(en in or)er

to *ro)uce memershi* functions that ga;e useful centroi)s for the 4nal results

9that is narro8 0aussians at the e)ge that gi;e numers close to 1.

-ame )eltaFor this in*ut I am s*ecifying the numer of )i=erent entries et8een t8o

aggregate names, ma)e u* of 4rst name, mi))le name an) last name. For

e7am*le, the name Samuel !ohn "eaysG 8oul) *ro)uce a ;alue of 1 8ith

Samuel "eaysG a ;alue of $ 8ith !ose*h Peter "eaysG an) a ;alue of & 8ith

6lizaeth Mary Coo(G.

The initial memershi* functions for this 8ill e a sigmoi)al function 8ith slo*e

;alue a H .?/ an) the interce*t *oint c H 1.?/. This is ecause ha;ing 1 name

match < 8hich in this case 8ill *ro)uce a ;ery 8ea( memershi* gra)e, is not

*articularly insightful. A lot of *eo*le share 4rst names, mi))le names an) last

names. >hen t8o names match there is a goo) *ossiility of a match 9es*ecially

if other in*uts are 4re). names matching is a )e4nite name match. The

sigmoi)al function ma*s this as sho8n in the a**en)i7. I too( some

e7*erimenting to get a slo*e 8ith the )esire) )egree of cur;ature ut this 8as

e;entually achie;e). The secon) memershi* function is no match, 8hich

naturally is symmetric aroun) $ ut in the o**osite )irection.

A))ress )eltaFor this in*ut I am s*ecifying the numer of )i=erent entries et8een t8o

aggregate a))resses, ma)e u* of the a))ress line 1, a))ress line $, a))ress line

, city an) *ostco)e.

The initial memershi* functions for this 8ill e a sigmoi)al function 8ith slo*e

;alue a H 1 an) the interce*t *oint c H $./ to get the cur;es to sit ush 8ith 1.

Again e7*erimental e;i)ence nee)e) to *ro)uce the a**ro*riate cur;e, an) the

no match memershi* function 8as again symmetrical aroun) < the mi)#. The

cur;e has een )e4ne) as much smaller ecause e;en one match et8een

)i=erent a))resses is li(ely to suggest a reasonale chance of a match, althoughit may e a to8n. In a real system there 8oul) e more in*ut ;alues for s*eci4c


6/21

;alues of the a))ress 8hich 8oul) ha;e a))itional rules, i.e. *ostco)e 8oul) gi;e

a high chance of matching, 8hereas to8n 8oul) gi;e a lo8 chance. For the sa(e

of this though only the a))ress )elta 8ill e of concern.

-I -umer e)it )istance

-I stan)s for -ational Insurance numer an) this is often store) in em*loyee orgo;ernment recor)s an) is a mi7ture of al*haetically an) numerical characters

J characters long . 6)it )istance here means the Le;enshtein )istance < 8hich in

a nutshell uses s8a*s, insertions an) )eletions 9all eDual to 1 to )etermine ho8

far a*art t8o strings are. 9'lac(, $%1 -I e)it )istance is J as this is the size of

the set 9assume all changes 8ere s8a*s. o8e;er it is generally assume) that

eyon) $ the chances of matching are ;ery lo8 an) e)it )istances eyon) $ are

almost certainly ne;er going to match. Therefore I ha;e )e4ne) a ;ery shar* set

8ith a sigmoi)al function on the left from % to 1%% 8ith a lo8 )egree of matching

on 1, e;en less on $, an) ;irtually nothing on % an) a no#matching memershi*

function 8hich is again symmetrical. The a**ro*riate measure ha) an a

*arameter of $% an) a *arameter of $.

ome *hone numer e)it )istanceThere are 11 numers ty*ically in a *hone numer so a ma7imum e)it )istance

of 11 is e7*ecte), 8ith the same *arameters as for the -I -umer.

0eogra*hical locationMany systems ha;e geolocation )ata. 0reat circle arc )istances of a))resses can

e use) to match *eo*le. There 8ill e three se*arate memershi* functions, a

sigmoi) for i)entical@ from %(m to (m to account for measure measure issues. I

8ill create another 8hich is *otentially mo;e)@ ase) on the assum*tion that

*eo*le mo;e ty*ically 8ithin $/(m or so, 8ith a stan)ar) )e;iation of $% (m. For

this it seems to ma(e sense to use a 0aussian memershi* function. Finally

there 8ill e a sigmoi) from i)entical to the en) of the range 8hich is )i=erent

location@. 0i;en I am assuming K" )ata a ma7imum )istance of 1%%%(m seems

reasonale.

0en)erThis is categorical )ata 8hich either has the ;alue #1 9not match or 1 9match,

8ith % as uncertain in cases 8here the )ata is un(no8n. This is a sigmoi) 8ith its

match in the centre 8ith memershi* gra)e % for oth at %./ for not sure, an) 1

for sure on either si)e.


7/21

ut*ut +arialeThe out*ut is a match )ecision. This is either no match, that it shoul) e sent to

a human )ata ste8ar) or match. Initially these are set as three e;enly s*ace)

0aussians, on the assum*tion that the a**lication of ;arious rules shoul)

*ro)uce nice e;enly s*ace) out*ut sets that 8ill )efuzzify in a relati;ely

straightfor8ar) manner )ue to their alance) nature, es*ecially un)er centroi)systems 8here the height of the ;arious 0aussian shoul) linearly mo;e the

)efuzzi4e) ;alue aroun).

3ules:The numer of *otential rules are:

R=ln

>here l is the numer of linguistic in*uts for each lael 93oss, $%%&, *. $?/. This

*ro)uces:

$ 7 $ 7 $ 7 $ 7 7 $ H J2 rules, 8hich 8hilst tractale can e re)uce).

In or)er to re)uce the numer of rules necessary to calculate this it is necessary

instea) to relate e7*ert Bu)gement of 8hen matches ta(e *lace. In other 8or)s

the s*eci4c scenarios that generate the three ty*es of outcome are )e)uce)

from my )omain (no8le)ge, translate) into logical rules an) *rocesse) as such.

Then it shoul) e chec(e) that e;ery comination has some (in) of e=ect, e;en

if this is )elierately to ignore in*uts that is are not useful unless in conBunction

8ith another in*ut.

ue to the relati;ely small numer of memershi* functions in each 9$ mainly

the numer of cominations is lo8er an) it is not necessary to use an)@ so much

< so metho)s such as the Com metho) or S+ )ecom*osition are not necessary

< an) a**ly to Sugeno ty*e inference systems ty*ically in any case. o8e;er,

once the t8o main scenarios ha;e een )e4ne), the use of the r@ o*erator

hel*s re)uce to a smaller size the numer of con)itions that fail to match, 8hich

8oul) other8ise ta(e u* a large ul( of the )e4ne) rules. Primarily the rules

ha;e een minimise) y consi)ering the con)itions un)er 8hich e7*ert o*inion

8oul) categorise certain )ata, an) then e7clu)ing the negati;e cases later on.

The follo8ing scenarios are regar)e) as eing a**ro*riate for an automatic

match, ase) on my o8n e7*erience 8ith con4guring MM systems:

There are four situations in 8hich automatic matching shoul) ta(e *lace:

1. When name delta is match and address delta is match and NI edit

distance is match then Matching is Automatch

>hen name, a))ress an) -I numer all match then it is almost certainly the

same *erson.

2. When name delta is match and address delta is match and

Geographical distance is identical then Matching is Automatch

>hen name, a))ress an) the geolocation )ata all match then it is almost

certainly the same *erson < the geolocation )ata corroorates a li(ely match.


8/21

3. When name delta is match and address delta is match and Gender

is match then Matching is Automatch

>hen name, a))ress an) the gen)er )ata all match then it is almost certainly

the same *erson < the gen)er )ata corroorates a li(ely match.

4. When name delta is match and NI edit distance is match andGender is match then Matching is Automatch

'oth -I e)it )istance an) gen)er suggest a match, ecause this comination

of three entries is *ic(s u* i)entical in)i;i)uals 8ho ha;e mo;e) a))resse) . 9$%%2, -o;emer. The What, Why, and How of Master DataManagement.3etrie;e) from Microsoft e;elo*er -et8or(:

htt*:ms)n.microsoft.comen#uslirary1J%12.as*7

Lilly, !. . 9$%1%. Fuzzy Control and denti!cation.>iley.

Lira, !. 9$%1. "#ternal Match.Informatica Kni;ersity.

3oss, T. !. 9$%%&. Fuzzy Logic$ with "ngineering %&&lications9$n) e)..

>hei#!en Chen, '. A. 9$%1&. 'uilding ()*+Degree nformation %&&lications.I'M

3e)oo(s.

>olter, 3. 9$%%?, A*ril. Master Data Management MDM- Hu %rchitecture.3etrie;e) from Microsoft e;elo*ment -et8or(:

htt*:ms)n.microsoft.comen#uslirary&1%?J5.as*7


13/21

A**en)i7 A: Memershi* Sets 4rst trial:-ame )elta:

0 0.5 1 1.5 2 2.5 3

0

0.2

0.4

0.6

0.8

1

name delta

Degreeofmembership

nomatchmatch

A))ress elta:

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0

0.2

0.4

0.6

0.8

1

address delta

Degreeofmembership

nomatchmatch

-I 6)it )istance


14/21

0 10 20 30 40 50 60 70 80 90 100

0

0.2

0.4

0.6

0.8

1

NI Edit distance

Degreeofmembership

matchnomatch

ome Phone -umer e)it )istance:

0 1 2 3 4 5 6 7 8 9

0

0.2

0.4

0.6

0.8

1

NI Edit distance

Degreeofmembership

matchnomatch

0eogra*hical )istance

0 100 200 300 400 500 600 700 800 900 1000

0

0.2

0.4

0.6

0.8

1

Geographical distance

Degreeofmembership

identicalidenticaldifferntlocation


15/21

0en)er

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

Gender

Degreeofmembership

matchnomatch

Match )ecision:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.2

0.4

0.6

0.8

1

Matching

Degreeofmembership

nomatch datasteward automatch


16/21

A**en)i7 ': Sigmoi)al0aussian m 4le:fuzzymdmfis=newfis('fuzzymdmfis');

fuzzymdmfis=addvar(fuzzymdmfis, 'input','name delta',[0 3]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',1,'nomatc','si!mf',[3"#$ 1"#$]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',1,'matc','si!mf',[%3"#$ 1"#$]);

fuzzymdmfis=addvar(fuzzymdmfis, 'input','address delta',[0 $]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',&,'nomatc','si!mf',[&"$ 3"0]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',&,'matc','si!mf',[%&"$ 3"0]);

fuzzymdmfis=addvar(fuzzymdmfis, 'input',' dit distance',[0 *]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',3,'matc','si!mf',[&0"0 &"0]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',3,'nomatc','si!mf',[%&0"0 &"0]);

fuzzymdmfis=addvar(fuzzymdmfis, 'input','+ome one um-er dit distance',[0

11]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',.,'matc','si!mf',[&0"0 &"0]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',.,'nomatc','si!mf',[%&0"0 &"0]);

fuzzymdmfis=addvar(fuzzymdmfis, 'input','/eo!rapical distance',[0 1000]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',$,'differntlocation','si!mf',[3"0

1"$]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',$,'moved','!aussmf',[&0"0 &$"0]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',$,'identical','si!mf',[%3 1"$]);

fuzzymdmfis=addvar(fuzzymdmfis, 'input','/ender',[%1 1]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',,'matc','si!mf',[&0 0]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',,'nomatc','si!mf',[%&0 0]);

fuzzymdmfis=addvar(fuzzymdmfis, 'output','atcin!',[0 1]);

fuzzymdmfis=addmf(fuzzymdmfis,'output',1,'nomatc','!aussmf',[0"0$ 0]);

fuzzymdmfis=addmf(fuzzymdmfis,'output',1,'datasteward','!aussmf',[0"&$

0"$]);

fuzzymdmfis=addmf(fuzzymdmfis,'output',1,'automatc','!aussmf',[0"0$ 1]);


17/21

A**en)i7 C: TriangularTra*ezoi)al 0aussian

Memershi* Functions

0 0.5 1 1.5 2 2.5 3

0

0.2

0.4

0.6

0.8

1

name delta

Degreeofmembership

nomatchmatch

0 1 2 3 4 5 6 7 8 9 10 11

0

0.2

0.4

0.6

0.8

1

Home Phone Number Edit distance

Degreeofmembership

matchnomatch

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0

0.2

0.4

0.6

0.8

1

address delta

Degreeofmembership

nomatchmatch

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

Gender

Deg

reeofmembership

matchnomatch

0 1 2 3 4 5 6 7 8 9

0

0.2

0.4

0.6

0.8

1

NI Edit distance

Degreeofmembership

matchnomatch

0 100 200 300 400 500 600 700 800 900 1000

0

0.2

0.4

0.6

0.8

1

Geographicaldistance

Degreeofmembe

rship

differntlocationmovedidentical


18/21

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.2

0.4

0.6

0.8

1

Matching

Degreeofmembersh

ip

nomatch datasteward automatch


19/21

A**en)i7 : TriangularTa*ezoi)al m 4le:fuzzymdmfis=newfis('fuzzymdmfis');

fuzzymdmfis=addvar(fuzzymdmfis, 'input','name delta',[0 3]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',1,'nomatc','trapmf', [1 1"$ 3 3]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',1,'matc','trimf', [0 0 &]);

fuzzymdmfis=addvar(fuzzymdmfis, 'input','address delta',[0 $]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',&,'nomatc','trapmf', [1". 3"$ $

$]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',&,'matc','trimf', [0 0 3"$]);

fuzzymdmfis=addvar(fuzzymdmfis, 'input',' dit distance',[0 *]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',3,'matc','trapmf', [1"3$ . * *]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',3,'nomatc','trimf', [0 0 $]);

fuzzymdmfis=addvar(fuzzymdmfis, 'input','+ome one um-er dit distance',[0

11]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',.,'matc','trapmf', [1 3 11 11]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',.,'nomatc','trimf', [0 0 3"*]);

fuzzymdmfis=addvar(fuzzymdmfis, 'input','/eo!rapical distance',[0 1000]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',$,'differntlocation','trapmf', [&$ &$

1000 1000]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',$,'moved','trimf', [0 &$ #$]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',$,'identical','trimf', [0 0 $0]);

fuzzymdmfis=addvar(fuzzymdmfis, 'input','/ender',[%1 1]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',,'matc','trapmf', [%0"& 0"& 1 1]);

fuzzymdmfis=addmf(fuzzymdmfis,'input',,'nomatc','trapmf', [%1 %1 0

0"&]);

fuzzymdmfis=addvar(fuzzymdmfis, 'output','atcin!',[0 1]);

fuzzymdmfis=addmf(fuzzymdmfis,'output',1,'nomatc','trimf', [0 0 0"$]);

fuzzymdmfis=addmf(fuzzymdmfis,'output',1,'datasteward','trimf', [0 0"$

1]);

fuzzymdmfis=addmf(fuzzymdmfis,'output',1,'automatc','trimf', [0"$ 1 1]);


20/21

A**en)i7 6: 3ule SystemThis Matla co)e a))s the necessary rules to oth systems:

rules = [

& & & 0 0 1 3 1 1

& & 0 0 3 1 3 1 1

& & 0 0 0 1 3 1 1

& 0 & 0 0 1 3 1 1

& 1 1 0 0 0 & 1 1

1 0 & 0 0 1 & 1 1

1 & 0 & 0 1 & 1 1

1 & 0 0 3 0 & 1 1

0 1 & 0 0 1 & 1 1

0 1 0 & %1 0 & 1 1

1 1 1 0 0 & 1 1 &

0 1 0 1 0 0 1 1 1

0 0 0 1 %3 & & 1 1

0 0 1 1 0 & 1 1 1

0 1 0 0 %3 0 1 1 &

1 & & 0 3 0 & 1 1

& & 1 0 3 0 & 1 1

& 0 0 0 0 & & 1 1

& 1 0 0 & 1 & 1 1];

fuzzymdmfis = addrule(fuzzymdmfis, rules);


21/21

A**en)i7 F Testing:-ample Matching

4el)s

3esult in

systemE

Matche) 8ith

fuzzyinferenceE

SuccessfulE

!amesFre)eric(Arhams

!amesFre)eric(Arhams

-ame characters, -I-umer,A))ress,0en)er

Automatch Nes -oThis e7am*lele) to thereBigging ofthememershi*function to*ea( at thee)ges

!ames

Ma)rigalsonFairuc(

!amesMo)rigalsonFairuc(

-ame $

characters,A))ress, ,0en)er

ata ste8ar)

referral

Nes Nes

6lizaethPo)rigal0inzer

!ames Toons0inzer

-ame 1character

Fail -o Nes. Althoughit )i) triggerone of therules for )ataste8ar)shi*the

memershi*;alue 8henonly 1 nameis )i=erent istoo lo8 totrigger 8hichis the )esire)result

fuzzy logic assignment 1

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