CLASSIFICATION OF OBJECTS BASED ON CASE

Yugoslav J our nal
~ ( HI~J ~ ),
I' () perat.i on s Research
Numbe r 1, 75- ~5
0
CLASSIFICATION OF OBJECTS BASED ON
CASE-BASED REASONING
,
Sanja PETROVIC
Un iversity of N oll inglia m
Com p u ter S cien ces Deportm en t
University Perl:
N G72HlJ United Kin g dom
Abstract: This paper presen ts a new approach to t he class ificat io n of objects which a n'
described by many features to one of tilt' categoril's in a preduter-mined set, of
categories. The classification is ba sed on case-based reasoning. Ra ther t ha n classify ing
new objects using necessary and su fficient conditions, defin ed by a set of \1.1I (·s , till.'
knowledge and expe r ience mcmorisod during past classification s an' used, Ea ch 1:,15('
com pr ises the description of the object and the category tu which it is assigued . 'l'h«
memorised cases are organised in a case base . In t he process uf classifying a new object,
a case which is the most sim ila r to the new object is re trieved from t he <.:< IS(' base . The
new object is assigned to t he sa me ca tegory as the r etrieved case . T he desci-ihcd
a ppr oa ch to classification was a basis for t he design uf an export system which helps
the decision maker classify a given multicriteria problem to an adequa te method fo r its
solving.
Keywords: Cla s sifi cation 01' o bject s, ca se-- based rea soning, mu lt icriteria a na lysis, Sf' lel' l ion 01' a
multi cr-iteria method .
1. INTRODUCTION
Variou s problems of operational research can he considered as classificatio n
tasks, where obj ects , described by many features, have til be assigned to one catego ry
from a predetermined set. of categories. The need for classifica tion of objects arises in a
wid e variety of domains , fur exam ple in machine repair diagnosis , medical diagnosti cs ,
loan applicant cla ssificatiun, and many uth er.
We fo cu s our research on the classifi catinn of objects based un cast· - !Jast·c!
reasoning tCHi{l. CHi{ is a new type of reasoning ba sed on the premise that h uma n
reasoning processes are founded on specific exper ience rather than a set CJf gl' n('ra l
7()
S . P et rovi c' / Classi ficnt.ion olO bjects Based on Case-Based Reasonin g
gu ide iines or first principles 181. In order to utilise past exper ie n ce, t he way s the
ex pe r ts solve actual problems from a domain are memorised as cases . CHI{ is preferred
for solvin g complex and ill- structured problems 1:31- Many classification tasks an'
ch a racte r ised by too much data available 01' by a lack of data with a large amount of
com plex or unknown interrelations among variables . Some data is hard to interpret or
qu a ntify. The refo re . many classifi cation tasks belong to t he class of complex and
ill- str uctured problems 111 . Usu a lly, t here are no algorithmic procedures , repetitive
a n d routine, which C<1Il produ ce one st r ict solu t ion for su ch problems . In t h e casc-- hascd
classifica t ion, inst ead of class ifying new objects using necessary and su fficie n t
cond it ions, which are no t always possible to define , the knowledge and ex pe r ie nce
meuuu-ised during pas t classifications are applied. One case comprises t he description
of t ill' object and t he category to which it is assigned . The m emorised cas es an'
llrga n ised in a ca se base . In the process of classifying a new object, a case which is t h«
IIlOSt s im ilar to the new object is retrieved from the ease bas e . The n ew obj l'ct is
a ss igned to t he same category as t he case retrieved. The new object is integrated in t he
casl!- hase. Therefore , the CHI{ classifica tion system learns incrementally and improves
its pe rfo r m a nce .
,
Som« in teres ting a pproaches to t he classification of objects in differen t
do m a ins based on CHl{ are described in the literature . The CHI{ svstem
PI{OTOS
•
pe r forms classification in t he domain of audiological di sorders 1141 . Given a description
of t ill' sym ptom s and test results of some patient. PI{OTOS determines which hl'm'ing
di sorder t h at patient has . PI{O'l'OS learns domain- specific knowk-dge under t ill'
gu icla n ce of an exper t who provides the addi tional information needed to rectilv
prob le m solvin g failures .
The re trie val of relevant previous cases is crucia l to t he success of CHI<
.s ystem, The u sefulness of previou s cases is dotorminod by assessing till' s im ilar ity of a
ne w ohject wi t h the previou s C<ISl'S. Differen t uieasu res of s im ila rit ies be tween cases
fr om till' ca se - base and a new object are conside red and tested u sing till' diugnosis and
repair tasks in an e lectrom ech a n ica l domain 1GI.
A novel nrc h itectu ro for com b in ing rule-bas ed and case- based rvasuuin j; is
prese nted in 151. Rules presen t hroad trend s in ti ll' domain . while cases are glHld tel
cupt u r« the exce ptions which viula to t he rules . TIll' principal idea is to apply till' rules
to a ta rget problem to get a firs t approxima tion of t h e answer. If t ill' prohlein is j u dged
to Ill' com p illingly s im ila r to a k now n exceptio n to t ill' rules in any a spect IIf its
lx-h uvior. the n t hat as pect is modeled after t he exceptio n ra ther than t ill' rules , TIll'
proposed a pproach is illu s trated in ti ll' domain of au to in surance whe re t ill' ta s k wa s t.1I
aSSI'SS the ris k of insuring a now clie nt,
Knowledgo a cquisition prohlcm s , syste ma t ic ca sc - hasod con struction and
ve- ri ficat ion of ex port knowl od gu l\I'l' treated in 191 and tested in m edical diagno sis
probll'IIlS.
In t h is pnper 11 new upproaoh t o cllsl,- llIISl·d cluss ificnt iun is dos cribod . TI ll'
proposl·d a pproach is a pp lied in t h« dou uiin of multicri torin unnlvs is lMCAl. T Ill'
v
S. P et rovic I Classi licat io n of O bject Based on Case- Base d Reasonin g
77
problem is to select an MCA method adequate for solving a give n multicriteria proble m .
The problem is treated a s a classification task, where t he description of eac h
multicriteria problem constitutes an obj ect which has to be assigned to one catcgu ry ,
i.e. to one among a number of multicriteria methods adequate for its solving. , ection :2
presents the architecture and the basic elemen ts uf the developed HR classifica t ion
sys tem. Section 3 describes t he developed CHR system MAG I ' (a cronym fur
Multicriteria Analysis !!uidance for Method Se lection Inferred from ~lIses l wh ich
a ssists the decision maker l lJMI in selecting an adequate M 'A met hod. An illu s tra t ive
exam ple is given with t he discussion abou t t he validation uf t he system. The u sefulness
uf t he application uf t he CHR in cla ssification problem s is pointed out in t he co nc lusio n .
2. CBR SYSTEM FOR THE CLASSIFICATION OF OBJECTS
Cla ss ifica t io n problems which are conside red in t h is research ca n be presented
in the following formal way .
Given: Object C is represen ted a s a conju nction of or dered pairs iindex, ualue i,
where indices are features of objects relevant for t he se lect ion of a catego ry :
C = ll i ndex, uoluei , I i E1Cl l.
Task:
Assign a given object C to one category from the set .'K = lK I •.. . · K AI : .
An index can be single-va lued or multivalued depending un the numbe r of
value s that can be a ssigned to it .
2.1. System architecture
Developing a CHR system which shou ld a ssis t in a ssigning a catego ry to a
particular object s tar ts with the identification of cases t hat can provide t he basis for the
classification of the new obj ect. For each category an expe rt provides a certain numbe r
of typical objects - prototypes which belong to the category and objects which a re
except ions to the category . They are treated a s t r a in in g cases . Given a new object to be
classified, the system proposes a category, matching t he new object against the cases in
t he case base . The object which is considered to be the most sim ilar to t he new object is
r etrieved. The category of t he re trieved object is proposed fur the new object. The new
object with t he proposed category is in tegrated in t he ca se base if it contains k nowledge
and exper ience not present in t he case base . In or der t o learn fr om past expe r ience , t he
CBR system has to collect feedback from the real world and tu t he notice conseque nces
of its reasoning. The category proposed may be eva lua ted as inadequate and then t he
CHR syst em continu es search in g the case base until some other category is proposed.
In this way, facing sim ilar problems , the system can avoid the sam e mistake in the
future and can propose the adequate category immediately . Learning from failure ,
which is realised in the developed CHR classification system, is an impurtant
7H
S. Pet.rnvi c I Class ifica t io n olO bject.s Baser! nn Case-Based Heasnnin g
cha racte ristic of CHK Three original algorithms are developed: n >an algorithm for
system training which integrates training cases in the case base and form s the initial
case base, l2) a n algorithm for the classificatio n of a new object and l:3) an a lgorithm for
learning from failure which continu es the classification process after the fai lure of t he
pro posed ca tegory is registered.
The CHR system developed consists of five main modules depicted in Fig. 1:
the inpu! module which accepts training cases a nd new objects, the iroi.nin.g m od ule
ami t he object classilication module which are used for system t rain ing and
classifi ca tion of a new object, the category module which contain s a number of
categor ies and is used to evalu ate t he proposed solu t ion, and the outpu t m odule which
presents the classification results.
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Figure 1: The architecture of the CHR classifica tion system
The remainder of this section gives a more detailed look at the CHI{ system
dove 10 ped .
2.2. Organisation of the c ase- base
•
The number of cases in the case- base ca ll becom e very large . In order to
«un hl« efficie nt sea rch of till' case- base the cases are organised hierarchically . During
t h« clnsxificut ion of a new object unly II sma ll relevan t su bset of the cases, cunsidorod to
' . I'p! rovic I C lassi li('al inn nf( lhj pcl s Basl,d un Ca sl,·Ba. l·d Hl' a Slln in ~
be t he most s im ila r to the new object, is re trieved , The s u hsct u I' ca ses
t hen he compared to th e new problem.
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Cases are hierarchically organised ill a sh urcd- feutu re not wur k . a s t ruct ure
which is known in the CHH literature lS I. Th e s luucd- fc ut u re ne t wo rk provi de-s II
means of clustering ca ses so t h a t the cases which have sum o cnn u u un inde x va lue-s an '
gr ou ped together. W(· u sed till' ge ne ra l induction principles ofl'e n·d hy t he LI 1M I~M
method fur incremental indu ctive k-arning 141 to co nst ruct t he uot work and umichod
t hem with some additional ch arac tc rist.ics necessary
fur CB H,
•
Each nude in t he ne twork is created by a ge ne ra lisation process perforu u«!
applying two cases . Th e ge ne ra lisatiun uf t he index values depends Oil t ilt' index ty p' ·~ '
The generalisation ex t r acts tilt' valu es of s ingle - va lu ed indices which an' equ a l ill bo t h
cases, and produces th e union of th« va luos of multivulu ed indices. TI ll' creutcd nu rks tores ti ll' cases and has indices which an' produ ced us t he rosult of t h e ge llt' ra li ~at i o ll
p r Ol.: e ~ ~ .
In the propo sed CB H alguri thll\ ~ , eac h node is n 'pl'l's"ll tl'd a ~ a u -ip l«
N = :rP .. fJ .C' : wh ere ()' is a su bse t uf ordered pai rs (ind ex, uuln c) which d l' ~t:rih, ' nud«
N , ()' = : ii n dcx, ualue i; li E 1,\' : , ,f! is a se t of node dosccndnnts, and (' is a ~( · t of t:a ~( ' :-;
sto red with the nude . Descendants of a node , i.e ., nodes on a lower h ierarch ica l le-vel ,
inherit all t he features of t ill' predecessor. odes un t he h ighe r leve ls of hic-rurchy
repres ent generalised con ce pts , while descending down t ill' hiera rchy more s pe c ifi c
con ce pts are reached.
The gual of the construction uf the network is to infer t he descript.iun of llodl':-;
from the description of a given set of ca ses . Cases are intcgrutcd in the presnn t
ne twork , one at a time , withou t re p rocoss iug previously e ncou ntered cases ,
2.:1. System training
An algorithm developed for the CB I{ system truining crea tes an ini tial s ha rr -d
feature n etwork ba sed on input training cases. Each training case is clas s ified into a
su ita b le ca tegorv .
Le t u s define the co nce pts which form t ill' basis for the CBH system t raining .
la) Importan ce 0 1' 0 11 ordered pairtindcx, value)
One of the crucial qu estion s for the clas s ificatio n of a new object is how mu ch
t he valu e of an index influences the se lect io n of t he category . It is a ss u m ed that till' s e-t
of ordered pairs sin dcx , value ) which churucte r ises object s is finite , To each ordered
pail' iindex , value) is nssoeiated to a coefficien t which re flects t he relative importance of
the index valu e in the se lect io n of the category. However, the nearest neighhour
method, often u sed in many CBI{ syste ms 1171 where a fixed weight is a ssncinu «! to
S. Petrovic I Classification of Objects Based on Case-Based Reasoning
80
each index and used in the similarity measure between a new object and cases in the
case base is not available. It can be noted that the frequencies of the appearances of the
ordered pairs (index, value) in the cases are different. Calculation of the importance of
an ordered pair (index, value) is based on the idea that if some index value occurs in the
cases which are classified into a large number of categories, or even into all of them,
then that ordered pair iindex, value) is not useful in the selection of the category. On
the other hand, if an ordered pair (index, value) appears only in the cases which are
classified into a small number of categories, preferably one, then that index value
characterises the category substantially and is very important for the category selection
process.
In order to calculate the importance of the ordered pairs (index, value> a table
of importance is defined, The rows of the table present ordered pairs (index, oalueu,
i = 1.
I, used in the object descriptions, while columns present categories,
KI
K/II ..... K M . To each field (i, m) a number n;/II is associated which presents the
number of cases in the case base which have the ordered pair (index, ooiuei, and are
classified into category K/II' The importance of each ordered pair (index, oaluei, is
calculated as the square root of the sum of the relative frequencies:
2
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Wi =
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/11 =
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ni/ll / ~ ni/ll
/11= 1
presents the conditional probability of choosing
category K m , if the object description has the ordered pair (index, valueJi.lmportance
lU i takes values from the interval 10,11, so that higher values correspond to more
important ordered pairs (index, ualueu, After the insertion of each case C in the case
base the weights lUi of ordered pairs (index, ualueu, i E Ie, contained in the case
description are modified.
( b)
Importance of a node
To each node is assigned a real value from the interval 10, 11 which expresses
its importance as a whole. The importance of node N is defined as:
W (N ) = 1 -
n (1 -
ui, )
t2)
i" IN
The more important the ordered pairs (index, oaluei], i E IN, node N has, the
closer the value W(N ) is to 1. If node N contains an ordered pair (index, ualuei; with
importance I, then W(N ) is equal to 1.
.
,
S. Petrovic I Classi ficatio n of'Objects Based on Case- Based Reasoning
( c)
•
81
Match relation
The match relation involves indices and it is defined in Table 1. The first
argument presents a valu e of the index in the network, the second one a value in a new
case (a training case , or a new object) . If the index is single-valued, then the match
holds true if the arguments are equ al. If the index is multivalued, then the match holds
t rue if t he first argument is a superset of the second one.
•
Table 1: M atch r elation
Index
Multivalued
single-valued
moichsualuetl, oalueil)
iff ualuetc
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ooluetl
iff valueN = oaluet)
(d ) Degree of the exact m atch between a node and a case
T here is an exact m atch between node N and case G if for each ordered pair
(inele.--r , oaluebi) contained in node N t here exists a pair (index, ualueil) in case G, and
t he relation m atchsoaluebi, oaluetl) holds true.
The degree of the exact match between node N and case G is defined as:
L W;.
;~
if there is an exact m atch between
Is
node N and case C
ExactMatchDeg (N .C ) =
13)
,
0,
other wise
If t he index is multivalued then the importance
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of the ordered pair
(ind ex , oaluet; in the node is defined as t he maximum of the importance of the index
and a ll values in t he value, se parately.
tel Match between a case and a n ew object
A case fro m the case base matches a new object if all of its index valu es are in
relation match with t he corresponding values of t he new object.
An algor it hm developed for the CBR system training incrementally updates
the shared-featu re network as input training cases are inserted in the system.
Updating means finding the place in the network where t he in put t raining case fi ts.
The algorithm developed is iterative by nature. Searching t he net wor k is based on the
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S . Pet rovic / Class ificat ion of Objects Based o n Case-Based Reasoning
defined concepts and heuristics 112 1, 11 3 1. The node with the larges t degree of exact
mat ch with the input t rain ing ca se is selected. Then, eit he r a new node is derived by
generalisa tion of t he inpu t case and one case of the se lected node chose n using t he
developed heuristics , or the input case is stored with the se lected node if the node
conta ins no case that m atches the input case.
2.4. Classification of a new object
The goa l of the classification of a new object is to find the node whose
description is t he most sim ila r to the new object and to match the new object against
the cases of the selected node . The ca tegory for the new object is proposed on the basis
of t he selected case.
The concepts used in the algorithm developed for the classification of a new
object a re in trodu ced below.
•
fa )
Si m ilar relation
A sim ilar relation is defined for each index using t he knowledge and
expe r ience of an exper t from the domain uf t he classification problem . T he first
a rgu ment concer ns a valu e in the network , the second one a valu e in t he new object. If
the object with value vallleN of a particular index is classified into one ca tegory and if
there a re reasons to classify in tu the same catego ry t he object with ualuet) of th e same
index. t hen sim ilaruial lieN , vallleC) holds.
The degree of th e sim ilarity between t wo index values can ta ke th ree values:
F ULL j vlATCH if the two values are equ al, PARTIAL _MATCH if t he valu e in the
network is sim ila r to t he new object value . bu t no t equa l, and NO_MATCH otherwise .
Parameters F ULL _MATCH , PARTIAL MATCH and N O_MAT CH are set a t 1, 0.5,
a nd O. respectively .
( b)
Deg ree ofIlu: partial m at ch bct uieen ~I n ude a nd a n cu i object
The proper definition of the s im ilarity measu re between a network node a m i a
new object is of gr eat value for good fun ctioning of t ho CI::\ H system. TIl(' s im ila r ity
ln-t wer-u the node and t he new object is expressed as t he degree of tilt' partial match
be twee n them . T he part ial mat ch e na bles a new object with no ma tch in t he case bast'
to hI' solved . The d egree of th e part ial match bettocen n ode N and /l CII ' object (' t ukos
in tu conside ration t he impo rta nce of t he index va lues of a node> which is s im ila r to t ill'
va lues in the new object a nd pu n ishes non- s imilarity . It is defined in till' fo llowing way :
l 'a ,.t i o IMa [{:h [)e~N (; ( N . C )
=(
I ii; ' lIIi
;t , ,\'(
wh ere :
~ IO ;
_ 1' ·
I
1 \ .(
)W(
T)
1·1)
S . P etrovic I C lnssi ficnt.in n o tOhiec t.s Ba sed o n Cas1"[lased Hea sonin g
1 NC
is a su bset of t he set I N such t hat for i
E
1 NC
.
oal uc in the ordered pair
iindcx, oaluei , is in t he similar relati on wit h the correspo ndi ng va lue of the
n ew object C
I ,ye
is a su bset of t he set I N such t hat fill' i
E
I NC , ualuc in the o rdered pair
Un dex, oalue i, is no t in t he simila r relation with the corres po nding va lu e of
t he new object C.
is t he degree of t ill' s im ila r ity between t he va lue of the index in the net wo rk
",
and in the new object,
is a parame ter expressing penalty when t he re is a difference between the
index valu e in t he ne twork a n d in the new object t the para m eter is set at ~ in
t he Ci H{ system developed ).
P
in order to direct the sea rchi ng process to more s pecific nodes wh ich contai n
more indice s and tu nudes wh ich contai n pai rs (index, vallie ) of highe r im portance , the
obta ined difference is multiplied by t he importan ce of the node ,
if t he index is mul t ivaluod , the n the im portance
W,
of the ordered pair
UI/(Iex , value); in a ne twork node is defined as the m ax imum of the impm -tance of t. h«
in dex and all valu es con ta ined in t he in tersection of t he ualuc and the new object va lue .
.s e pa ra te ly.
\c )
Degree oft he p ort ial mu tch beiuiccn a case and a ncui object
or
T he d egree
th e partial match bcttcccu a case C1 and a ncu: object C~ is
defined in an analogou s way :
Partia IMa lchDcg CC(C l. C 2 ) =
L Si ·/lJ i - I' . ~/IJ ,
i· I , ,! , ..o'
I
,
,
I fj I
I/" ~
where :
is a su bset of till! se t I C ) such t hat for i
1 ( . ](, '2
'= 1 ( ' 1( "2 '
ua luc in tho orde red pa ir
u.ndcx. oalue i; is in the similar re latio n with the correspo ndi ng valu« of the
n ew object C2,
is a su bset of the set 1(.') such t hat fill' i E 1(')(; '2 ' oa l uc in the o rdered pair
tinde.x, oalue i; is n ot in the simila r relation with th e cui-respondi ng va lu e of
t he new object C2.
T h e algori thm developed for t he classifica ti on of a ne w object propagates the
in dex valu es of t he n ew object to a n existing network using defined co ncepts and
he ur istics 1121, 11:31. The node wi th t he larges t degree of partial match with the new
object is se lected . T he case of the selected node wit h the h ighest degr ee of pa rtia l m a tch
with the new object is retrieved. T he category of the re t ri eved case is proposed for th e
new object.
,
84
S. Petrovic / Classification of Objects Based on Case-Based Reasoning
In order to control the growth of the case base, rules are defined to determine
whether the new object has to be memorised or not 1121. Generally, a new object is
integrated into the network if it contains knowledge or experience not already present
in the case base.
Training cases and the order of their insertion in the case base influence the
network st r ucture and the descriptions of the nodes. An induction process has to
identify all the indices which should not be in the node because of their irrelevance for
the categories under the node. In order to accomplish this, fine tuning of the node
descriptions is performed during the system training and new object classification. A
certain ty factor is assigned to each index in the node. In the algorithm for the system
t raining, the certainty factors of all indices in the selected nodes are increased by 1.
After the completion of the training phase the certainty factor of the index in the node
is equal to the number of the cases stored under that node in the hierarchy. The
certainty factors associated to indices in the nodes selected during the search are
updated accordingly. If the value of the node index is similar to the value in the new
object, with the degree of similarity FULL_MATCH, the certainty factor of the index is
increased by 1. No' change is made if the value is similar with the degree
PARTIAL- MATCH. If the value of the node index is not similar to the value in the new
object, the certainty factor of the index is decreased by 1. When the certainty factor of
the index drops below a specified threshold then this index is not relevant for the
ca te gor ies under the node hierarchy. The index is therefore removed from the node.
Removal of the index can cause two nodes in the same hierarchical level to have the
same description . Such two nodes are joined and a new node which contains the union
of the descendants and the cases stored with the two nodes is created.
3. CBR SYSTEM FOR SELECTION OF AN MCA METHOD
In many real-world problems there is a need to analyse a finite set of
alternatives described by many criteria. Criteria are u sually expres sed in different
units of measures and different scales and they are totally or partially conflicting and
incommensurable. The aim of MCA is to help the DM explore the multicriteria problem
at hand, express his/her preference st ructu re , and even tually lead to a preferred course
of action .
Over the past two decades many MCA methods have been developed 1161. It is
est imated tha t there are more than 50 distinct MCA methods 1111. A large number of
MCA methods have arisen not just because of different schools of thought that have
differen t ideas for solving multicriteria problems, but also from diverse views of DMs
and various preference information they enter into analysis. Conseque nt ly, t hose
methods are not easy to classify, eva lua te and compare. But, despite the development of
a large number of methods, no single one can be considered a su per ior m ethod,
applicable in a ll decision making situat ions. Many analysts art> not able to clearly
justify t he ir choice of on e MCA method rather than another. Very often the choice is
mot ivnted by familiarity with 1\ specific method. This means that the decision making
situat ion adapts to the MCA method and it shou ld be the opposite - within the set of
S . P etrovic I Classificat ion of Objects Based on Case- Based Reasoning
l:l5
MCA methods an analyst should select the MCA method adequate for 1I given situa t ion.
Therefore, there is increased interest in the formalisation of a process whose aim is to
assist the DM in the selection uf an appropriate MCA. and in implementation of all
appropriate soft ware package .
Expert system technology offers variou s techniqu es tu sim u late the behaviour
uf an expert in MCA. Rules arc very often u sed in ex per t systems fur knowledge
r epresentation. However, the large number of methods , the diversity of multicrit eria
problems and the large number uf problems that are except ions to 1I typical applica tion
uf an MCA method, r equire a large number uf rules which arc cu m hersomo and tediou s
tu define , modify and maintain .
Instead, the prototype system MAGIC based on the described casu- based
classification was developed. MAGIC was developed u sing the obj ect-oriented
programming language C+ +. MAGI C introduces six rather popular M CA me thods :
ELECTRElll151, PROMETHEEllI21 , t he Conj u nctive method, Maximin, TOPSI S ,
and SAW - The Simple Additive Weighting Method 171- The modular structu re of
MAGIC ena bles r elatively easy incorporation of new MCA methods.
The introduced M CA methods require the following preference infurmation
from the DM: weights which present the relative importance of criteria, acceptable
levels which present cutuff values acceptable for ea ch criterion, indifference th resholds
with re spect to a single criterion - u sing this parameter the DM expresses his/her
indifference toward t he difference between the cr iter ion values uf t wo alternatives . and
preference thresholds with respect tu a single crit erion - u sing these parameters the
DM expresses his/her attitude toward the difference between the criterion valu es of
two alternatives to consider that one alternative is s t r ict ly preferred over the other.
Indices used to describe the cases of multicriteria problems which can be solved by t he
introduced MCA methods arc given in Table 2. Index cri type is multivalu od , while all
other indices are single-va lued.
Table 2: Indices u sed to describe MCA cases and their domains
Index
Description
probl iype type of the multicriteria problem
linguistic term used to ex press the problem
num. or
alter
dimension taking into account number of
alternatives
nuni or
linguistic term used to express the problem
all
dimension taking into account number uf
criteria
cri type
type uf criteria valu es
weights
exist e nce of criteria weights
exist ence of criteria cutoff values
ac e level
indiff
existence of indifference thresholds
existence of preference thresholds
pre]
Domain
{rank, class . best , seoeral ;
lsmall, m oderate, large:
:small, m oderate , large:
Icard, lin g ; bill :
{yes, /10 I
[yes, 11 0 1
: yes, /10 :
{yes , no :
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Table 4: Training
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S. Petrovi c / Classi fication of O bjects Based on Case- Based Reasonin g
88
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S . P etrovic / Classi fication nf Object s Ba ed n n Case- Based Reason in g
I'l l
If cases are in tegrated in the ca se base un t he basis of t he problem type they
solve, then the shar ed- fea tu re ne twork presen ted in Fig. 2 is obtained, The ta ble of
importance is presented in Table 5.
Table 5: Table of importance after in sertion of the training" cases
•
Index
I
COlljU1I -
,
ELECTRE
PROMETHEE
J', t Cl.'"C; 111 ; 11
TOPSIS
SAW
2
0
1
0
0
1
1
1
0
0
:3
0
2
1
0
0
-0
2
0
1
1
0
2
2
0
0
0
-
I
:j
0.49
clive
II .
probl type
clas
1
2
3
4
1
0
5
6
7
0
0
:3
:3
0
0
8
9
10
3
0
0
2
0
1
3
0
0
-0
-0
0
0
0.46
1
1
;j
0 .58
card
11
12
13
2
2
1
3
'0
0
3
2
0
3
0
0
2
1
0
0 .42
lin/{
bin
2
1
0
weigh ts
y es
no
14
15
0
3
3
0
3
0
0
:3
3
0
::1
0
0.5
0.7 1
ace level
y es
no
16
17
1
2
0
3
0
3
0
:3
0
0
I
;j
;j
0.4 1
18
19
0
3
0
3
2
1
0
3
0
0
I
;j
;j
0 .42
20
21
0
3
0
3
2
1
0
3
0•
3
0
3
I.
ranle
best
severa l
'WIll
0
2
0
I
'J
0 .75
0 .6 1
0.5
0.75
o] alt
SI1l a ll
moderate
large
nUI1I of at t
sm all
mod era te
large
.)
?
0 . 5 :~
-
o tt type
in di ff
yes
no
prcf
y es
no
0 . 5 :~
I
0.42
In order to en able learning and to successfu lly use previou s experi e nce in the
new problem solving, the proposed M eA method is eva lua ted. The proposed met hod is
eva lu a ted as inadequate if:
1)
Some of the input data required fur the method applied are no t give n in the
new problem . Fur exam ple the DM did nut specify the relative importance of
criteria, but the method proposed requires them .
~.
! II I
P etrovi c' / C la s s ifica t. inn "rOhjects Based on Case- Buse d Heasnnin g
'2 1 'l'h e proposed m ethod doe s not include all input data . 1"01' exam p le the UM
s pec ified the acceptance level for all criteria , hut the m ethod proposed doe s
no t u se t hem.
;{ I
The OM , on t ill' ba sis of his su bject ive judgement, asks for so me other
me thod to solve the I,,' ;ve n problem .
The syste m continues sea rch ing the ne twork un til an adequate category is
proposed. The algorithm fur learning from failure is developed 1121 . The new object
w it h an adequate category is integrated in th e network in the appropriate place .
s. I.
Example
The proposed algorithm for cln ssificution of a I\{'W object is illu strated with an
«x mn p lc. WI' have st a ted a very cu rre n t problem of the se lect io n of the hest mohikphone st a t io n. There are• now at least 10 different sta t io ns on the market. The criteria
used m e : price , weight, volum e , and life of power su p ply. All of them are described hy
curd ina l valu es . 'I'he problem MSI which has to Ill' so lve d is I,,' ;ve n a s :
MSI
= t ip robl /.VPI', best), in u rn ojaltcr, m oderate) , in tn n cfcri, s mull ),
tCI'i type, :ml'd:), ltOt·iJ.!ltIs . yl's),
((1( '( '
lcocl,
I/U).
til/ d ill:
n o ),
iprc],
I/ O )
l.
Lrt u s su ppos« t hat t ill' caSl' ha sl' is prosc-n u-d by t ho sh a recl- foa t u ro n e-twor k
dl'p ictl·d in Fig . '2.
In t he firs t step of t ill' algorithm t he dl'b'1 'l'l's of t ho part.inl match hctwoon t ill'
dl'sC( 'ndlln t s of node Nt and t he prnhlom MSI are cnlcu luted:
= 0 .'2'2
l'uI'/ ioIMo/('hf)cgNC'(N:{ , MSI 1 = 1.5'2
l'uI'/iuIMo/ chf)egNC'(NG , MSl 1 = UJG
l'ol'/ioIMo/('hUcgN('(N'2 , MSl )
1'(lI'/i(lIMu/ <:h/) I'~N(, (NII,
M.",') ) = '2 ,'28
Nud« Nil is so le ·t('d lind sea rc h ing till' network co n t in ues. Furt.lu-r lin , nudo
N 14 is sl' lr 'ctl'd . Nude NIt! cu n t u ins no descendants , hut hlls two cases : 'l'OI'SI,'-,') suc h
t.ha t. l'ol'//(dMu!c ·h f)l'gC'(,'('I'() I 'SIS I , M S l) = :1.4 0, and I!-'U','("I'Hl~''2 s u ch tha t
l'II I'/ i (/IM u/ ('hlJ('g CC'(/~'U';('THI'::2 , MSI 1 = :lA O. Both cas('s have t Ill' sa u u - dl'gl'l '(' of
pa rt ia l m a tch with t he new ohj('d and tlu- syst or u firs t propOS('S tlu- TOPSIS me-thud .
«w ohj('ct MSI is s tn ro d wi t h nCl(Il· NIt! , hc cnu s« it dol' S no t mat ch till' cas('s s to red
with thut. nud«,
Lot, u s SUPPOS(' t luit SOIJ H' nddi tiounl l'rit('ria uro included in till' ulu-rnutivos'
r-va luut.ion : d('sign , ro lia h ility, uudihili ty , l' ' ist(' nl:\' of 111I in tc-rfaco to ti ll' huuuui USl'r
fili i 'l'lIph Il IH', loud spl'ak ('r , di spilly , I'te . l, lind oxi st.ouco Ill' all interfa cl' to o ther torrniuu]
pq u ipll lt' nt tl' e , lucsimil« m uchin o, I't ·.l . 'I'lu - values of t h« first t h l'('(' cr ite r ia an'
S. P e t rn vic I C lnssi fi cat.in n nfUbj ects Based o n Ca se -Bu sed rh'a~n nin ~
!,I
lin guis tic, while the four t h a nd fift h arc binary . The prob le m M .S'2 which ha s t il IJl'
solve d now is more comp lex:
MS'!. = ( iprobl
( 11 11 111
type, best ), ( 11 11 111 or a lt er, m oderate) ,
ojcri. m oderates , icri type, ico n] , lin g , bi n; J. ituciglit«, ycs) .
(0<:<: l evel,
11 0 ) ,
(;lI d ill:
11 0 ) .
(p re!:
11 0 )
I,
Node s NIl and N it! arc se lected again . The degrees of t ho partial
be tween the l.:<ISeS of node N 14 a n d the problem M B2 a rc ca lcu la tccl:
II 111 t ch
= 1.91
f'ar/i o IM a /<:hlJeg C Cr['O}JS/Sl , MS'!. )
f'ar/;oIMa /chlJcg C ('( t.'Lf<X TU /!;'2 , MS2 1 = :3.75
= '2 .64
f'or/ ; oIMo /<:hLJcg C'C(MSl , tvl.':i2 )
Ca se /!;L/!;C'1'H If:2 is sele cted a s t he must s im ila r to t he o bject /1'18'2. 'I'h«
existe nce of linguistic and b in ary cr iter ia in object Atl S'2 influ ences the proposa l o f the
method. Inst ea d of t he TO PS IS m e thod , the ~L8CT}{E me thod is s uggest ed t il so lve
t h e prob lem MS'!. . Prob lem M B '!. is s to red wi th t he node N I4 . The part of the ne twork
modified after solvin g t h e prn h le m s M Si and M S 2 is s ho w n in Fig . ::1 .
probl
1111111
cri
.V I
node
N Il
best 5
nf cri : 1'1111111 -I
ZI'/It ' : card, /illg. hili
typ«:
we ight »:
(ICC
notle
)'e,,'
level:
110
:I
"
,
""
PR01H3
node
o f alter:
uulif•]: . 110
-I
pre]: li n
-1
/ /1/1/1
N 1-1
.1'1/10 1/
•
#-
EL ECTRE2
I;
MS I
~
M S2
""
TOPS/SI
Fib'llre :-1: P art of the ne twork m odified a fte r solving t he pro ble m s
M SI a n d M B2
•
S . P etrovic / Classificat.ion ofObjects Based on Case-Based Reasoning
:-1.2. Validation
The validation of the CHi{ system is basically very sim ilar to the ex pert
systems va lida t ion with a specificity resulting from t he dynamic character of CHR The
validation of an ex pert system ge ner a lly involves running a set of representative
problems t hr ough the system and com paring system outputs to the known r esults or
hu ma n expe r t solutions.
The awkward st ru cture of the MCA problems , particularly the fact that some
mu lticriteria problems can be solved by more than one method, makes the validation
delicate . In addition , the case base is continuously enriched with new ca ses causing
dynamic changes of the CHI{ system behaviour and thus making the validation eve n
more com plex. As there is no firm theory used f(JI' the se lect ion of an MCA method, the
va lida t ion of the CHi{ system requires the validation of every single problem-case .
The prototype the CHI{ system was trained in two different ways u sing the 18
tra in ing cases presented in Table 4: 0 ) the training cases were inserted on the basis of
t he method used for the problem solving and l2) the training cases were inserted on the
basis of the types of problems solved. In this way , two different sha red- feat ure
networks were crea ted , MethodsNct and Problemsblet , based on the same set of t ra in ing
cases.
Two sets of test cases are specified and used in t he validation process .
a)
The set of test problems which are no t con tained in t he case base
The fir st set of t est problems contains 18 represen ta tive new problems not
conta ined in t he case base , pro vided by an ex pert in MCA. The new problems shou ld he
solved by t he s ix m ethods introdu ced in the prototype CHI{ sy stem. The classifica tion
resul ts are presented in Table G. Using the network MelhodsNet , t he system proposed
t he sa me methods as the expert did for eleve n new problems . Two problems were
class ifie d to methods which ca n be u sed for probl ' JIl solving, althou gh t hey were
differen t from the expe rt' s choices . Five new problems were classified to inadequate
me thods , hut after additional sea rch ing, the second proposals were equa l to t ill'
expe r t's opinion . The ne twork Problems N et coincided with the ex per t's proposals in
fuur t 'en new problem s . Once the proposed method was adequate. althou gh different
from t he expe rt' s proposal, and in three new problems the seco nd proposals were equ a l
to the exp 'rt' s.
Table 6: Classification resul ts for t he 18 test probl nn s no t conta ined in the ca se base
Melh udsNel
Probl elli s el
Syste m solu t io n coinci d ' H with ex pert's
11 lG 1. 11 %)
14 l77. 78'f'o)
Adequate me thod is proposed , hu t differen t
Irom expe rt's proposa l
20 1. 11%)
1 l5.55%l
dt'lfua tt' me thod is proposed a ft<' r failure
5 l 27. 78'i{,)
:J l lG. G7%)
S , P etrovi c / Clnss ifica t ion o lO bject.s Ba sed o n Cuse-Ba I,d Reasouuu;
h)
The se t of test pro b lem s which are conta ined in the case base
•
The aim of the second set of tes t probl ems is to exam ine th e boha viou r of t. luCHH system in t he classi fica tion of a new prohl cm which mnt chcs a case a lready
prese nt in t he case base. Fo r t hat pu rpose, each t ra ini ng case is t reated a:- a ne-w
pro blem . T he order of their classifi ca t ion is take n randomly. It is tested whet her the
re trieval process will give a case that matches the ne w prob lem . Th ' followuu; re su Its
are ob tained and prese nted in Table 7. Using the networ k M eth odstvet , in Hi ou t of I H
new problems the syste m retrieved t he ir cor respo nding cases from the case hnso. In on«
in stance, t ill' expected m et hod was proposed a ltho ugh not by t he correspo nding ca sp,
a nd in another in stan ce t he a dequa te met hod was obta ined in the seco nd pro posal. TIJ('
network Pro blcmeN et s howe d eve n bet te r pe r fo r ma nce. In a ll of them tilt' correctness
of reaso ning was proved a nd the cor res po nding cases were s ,I -cted .
Table 7: -:las sifilAltion resul ts for 18 new pro blems contai n ed in the lAIS ' bas '
M et hods N et
Problenisivet
I G l88.90'}(,)
18 ( 1OO'X)
Adequat e met hod is proposed , a ltho ugh
re trieved lA1Se does not ma ch the new prob lem
1 l5.55%)
0
Adequat e m ethod is proposed a fter failure
1 l 5. 5 5';~)
0
Retrieved lA1Se matches the new pro blem
We ca n notice that u sing the sp ecifi ed traini ng a nd test cases till' net work
Pro blemsblet showed bet ter per fo rm a nce.
Va lida tion shou ld no t he considered as a binary decision va ria hlo whi ch shows
whet her the system is absolu tely va lid or invalid 1101 . Since expert syste ms re pre "(' nt
or abstract t he reality , a perfect performance ca n not be expected. In some situa t io ns,
th e a cceptable performance range ca n be specified by the system user. For exam ple, till'
u ser may require t he CHl{ system to always correctly classify mul ti cri ter ia pro blems of
a particu lar type , and to be more to lerant of t he incorrect classifica t ion of ot her
pro blem types. Further, t he pro ba bi lity of a pa rticu la r incorrect classifica tio n may 1)(>
im portant. f or exam ple, it may he vita l that the system does not clas sify t he probl em
in to MCA meth od B if the correct met hod is A in more tha n 20% of the cases - that is
fJ(B I A ) < 0.2 .
It ca n be concluded that the MCA CHI{ system pe rfo rm a nce is quite good ,
especia lly if we t ake in to conside ratio n tha t the tota l numb er of cases in the ini tia l case
base was not large. The problems whi ch fail ed to be cla ssified to a dequate methods in
t he first proposals were integra ted in the net work in places which ena ble t he same
mistakes t o be avoided in future sim ila r prob lems.
S . Petrovic / Classi ficat ion of Object s Ba sed o n Case- Based Rea sonin g
~J4
4. CONCLUSION
T he philosophy, concepts and t echniques of CBR, originally appearing in
cogn it ive science and com pute r science, are applicable in the OR dumain . It is shown
t ha t CBl{ is u seful in t he classificatio n of problems. The proposed case-based
classificatio n is illu stra ted in solving t he import an t and a ttractive problem of t he
select ion uf an adequate MCA method fur solving a given multicriteria pro blem .
Reasoning in the CBR classificatiun system relies on exper ience in t he problem domain
rath er than on formal models and rules. The knowledge acquisitiun process , which is a
bottleneck in the expert system development , consists mainly of memorising t he objects
classified. In the CBR classificatio n system t wo processes are integrated: (L) the
classification of a new object in which an adequate category is selected, and l2) the
learning process which modifies the network st ru ctu re and node descriptions as the
consequences of knowledge genera lisa t ion and knowledge tuning. The system learns
from both kinds of expe r ience , success and failure, and thu s avoids r epeating mistakes
made in solving previous problems.
•
Further CBR system developments will include t he in corporation of additional
MCA met hods a nd consideration uf a com bination of methods in or der to include a ll
characteristics uf new MCA pro blems.
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1.1 1
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17 1
pq
1111
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