Research Article Selecting e-Purse Smart Card Technology via Fuzzy AHP and ANP - Hindawi

15 Pages·2015·4.49 MB·English

Hindawi Publishing Corporation
Journal of Applied Mathematics
Volume 2014, Article ID 619030, 14 pages
http://dx.doi.org/10.1155/2014/619030
Research Article
Selecting e-Purse Smart Card Technology via
Fuzzy AHP and ANP
NurgülDemirtaG,FenimÖzgürler,MesutÖzgürler,andAliFuatGüneri
DepartmentofIndustrialEngineering,YildizTechnicalUniversity,34349Istanbul,Turkey
CorrespondenceshouldbeaddressedtoS¸enimO¨zgu¨rler;[email protected]
Received19November2013;Accepted9March2014;Published1June2014
AcademicEditor:HuijunGao
Copyright©2014Nurgu¨lDemirta¸setal. This is an open access article distributed under the Creative Commons Attribution
License,whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperly
cited.
Developmentsintheinformationtechnologiesprovideimportantadvantagestoconsumersandcompanies.Nowadays,smartcard
technologystartstousee-purseapplications.Theaimofthispaperistoidentifythemostimportantdecisioncriteriatoselect
thebestcardtechnology.Inthisstudy,atfirstsmartcardandmultipleselectiontechniqueswereexplained.Thenthebestcard
technologywasselectedforane-purseapplication.Thethreetypesofcardtechnologieswereexaminedandthemostimportant
criteria were taken into account by the software developer while they develop card software. Fuzzy analytic hierarchy process
(FAHP)andanalyticalnetworkprocess(ANP)techniqueswereusedtocomparesmartcardtechnologies.
1.Introduction Smartcardisbeingusedinlotsoffieldsincludinghealth,
security,retail,telecom,banking,government,andautomo-
Analysis with single parameter or criterion is not enough tivefield.Besidethisfunctionalusage,innovativeapproaches
to resolve the complex structured problem parallel to the havebeenexploredwhiletraditionalboundarieswerepassed
developmentofscienceandtechnology.Themostsignificant over in retail segment. While exploring these approaches,
inferenceofthesingle-criteriaanalysisistoaccepttheother technological improvement and especially development in
dimensions of the event as static and to examine only one theinformationtechnologiesareusedasexploitable.
factor for each time. However, the events and the objects Developing smart card application including card pay-
occurundertheinfluencesofahugeamountofinternaland ment system and card personalization should demonstrate
externalfactorsinsteadofasolitaryfactoranddemonstrate multicriteriastructure.Multipleparameterjudgmentmeth-
complexformation.Becauseofthisreason,eventsandobjects odsareappropriateforsmartcardtechnologyandbyusing
mustbedefinedaccordingtotheamountofagentsandtheir these methods choice of smart card technologies should
collectiveefficiencyratherthanasingleagent[1].Duetothese presentmoresensibledecisionsandsuggestions.
factors, multiple parameter judgment methods are applied The rest of the paper is arranged as follows. The smart
in almost every field. And one of these fields is smart card cardtechnologywhichisappropriatefordevelopinge-purse
technology. application is presented in Section2. In Sections 3 and 4,
Usage and effectiveness of internet is increasing day by FAHP and ANP methods are explained, respectively. In
day. One of the important results of this frequency is that Section5,thesemethodsareappliedinordertoselecte-purse
the commerce is moving to the electronic environment. smart card technology. Finally, the results of the paper and
Transferring the development of the information technolo- futurestudysuggestionsareconsideredinthelastsection.
giestotradeiseffectivelybeneficialforbothconsumersand
companies.Smartcardtechnologyhasbeenbuiltupbecause 2.SmartCardConceptandProperties
of the necessities plus these benefits. Development of the
smartcardtechnologieshasbeenincreasingsinceitstarted 2.1.SmartCardConcept. Technologicaldevelopmentiskind
tobeusedin2002intheworldandTurkey. of“minimizingautomationsystem”process.Communication
2 JournalofAppliedMathematics
Contact smart card
Combi card
Contactless Contacts
Chip
chip
Antenna Chip
Contactless Antenna
smart card
(a) (b) (c)
Figure1:(a)Contactsmartcard,(b)contactlesssmartcard,and(c)combicard.
technologieslikecellphones,smallbutfunctionalcomputer card[8].Contactcardsuseaneight-pincontactmicromodule
systems,microchipsmanagingandcontrollinghugemecha- tophysicallyconnecttothecardreader[8].
nisms,anddatabaseunitsaretheexamplesofthisminimizing
automation.Smartcardwouldbeincludedinthisminimizing
2.2.2. Contactless Smart Cards. Contactless smart cards as
automationprocess.
showninFigure1(b)[9]useanantennawithapproximately
Smart card technology has evolved a long way since a10-centimeter(cm)rangetocommunicatewiththereader.
the idea of using plastic cards to carry microelectronic These credit-card sized memory-chip devices derive their
chips was patented back in 1968 by Dethloff and Gro¨trupp power from an RF field generated by the card reader. The
[2]. A smart card is a credit-card sized plastic card with RF field also transfers information to and from the card
an embedded computer chip that can be memory or also and card reader [8]. Contactless cards are better suited for
include a microprocessor[3–5]. A microprocessorchip can environmentswherequickinteractionbetweenthecardand
add, delete, and otherwise manipulate information in its readerisrequired,suchashigh-volumephysicalaccess[10].
memoryandhenceoffercomplexdatasecurityschemes[4]. Employeeidentificationbadgesissuedbylargecompaniesfor
Smartcardtechnologycanenableanorganizationtobecome buildingaccessaretypicallycontactlesssmartcards[8].
more secure, efficient, and interoperable while delivering
strong authentication and security, identity management,
2.2.3.CombinationSmartCards. Multipurposecombination
data management, customer support, and communications
smartcardsareahybridmixofthecontactandcontactless
[6]. The card body is usually more than just a carrier for
designs [8]. These cards obtain the two systems described
the chip module. It also includes information for the user
above. These cards contain all the properties of the other
and card accepters and of course security elements for
two types. Figure1(c) shows the combination smart card
protection against forgery. The card elements are printing
[9]. They include the eight-pin contact for communication
and labeling, embossing, hologram, signature panel, tactile
with a contact-type reader and also include an antenna for
elements, magnetic stripe, chip module, and antenna [7].
communicationwithanRF-typereader[8].Withsuchacard,
Smartcards,theresultofevolutionofmagneticcardinuse
it becomes possible to access the same chip via a contact
ofdailylife,havesuperiormemorythanmagneticcards.This
and contactless interface, with a very high level of security.
vast memory provides ability to execute lots of functions
It may incorporate two noncommunicating chips—one for
and present complex result. As a result of this condition, a
eachinterface—butpreferablyhasasingle,dualinterfacechip
databaseforcustomerrelationshipmanagement(CRM)and
providing the many advantages of a single e-purse, single
statistical data network can be provided by installing all of
operatingarchitecture,andsoforth.Themasstransportation
the information of any customer. Also it becomes easy to
and banking industries are expected to be the first to take
reachcustomeralmostineverybranchofbusinesslikehealth,
advantageofthistechnology[9].
automotive,andretailsector.
2.3.AdvantagesandUsageAreasofSmartCardTechnologies.
2.2. Smart Card Types. A smart-card chip communicates
Smart card automation process has lots of function such
with a reader by direct physical contact or by a radio
as; to prevent time lost, to reach customer, to control effi-
frequency(RF)signal,dependingonthesystemdesign[8].
ciency. Working level becomes mobilized with smart cards.
Smart cards are grouped into three classes for chip-to-
This means workplace is not bounded to an only place
readercommunicationswhichare(1)contactsmartcards,(2)
and customers are reached every time. Briefly, customer
contactlesssmartcards,and(3)combicards.
relationshipmanagementbecomesthefocusofbusinessand
productionprocessanditseffectivenessincreases.Smartcard
2.2.1.ContactSmartCards. Contactsmartcardsarethemost usage provides trust and prestige to company or company’s
popular card-connectiondesign and are used for both card institutional identity. Smart cards are more secure than
sizesandchiptypes.Figure1(a)[9]depictsthecontact-type magneticcards.Thehighlydevelopedsoftwareofsmartcards
JournalofAppliedMathematics 3
raisessecuritylevel.Incasesmartcardsareobtainedbythird
Payment cards
person, risk of data theft is decreased by the software that
preventscopyingdataandprotectsthecryptologyalgorithm.
Information stored in smart cards is protected by complex
security mechanism. Because of this reason it is hard and
expensive to copy or change data. Progression to smart Credit cards Debit cards Electronic purse cards
cardfrommagneticcardsdecreasesthecardforgerycaused
by both fake cards and offline card process. During the Figure2:Classificationofpaymentcards.
mobilized usage, the most important necessities are data
security and accuracy. Disability to copy and change data
in the card and to reach data during service is the most
importanttonotethatconsumeracceptanceandconfidence
significantproperty.Itisvitaltoprotectbothcardownerand
are crucial for the further development of smart card tech-
serviceprovider.Smartcardscanprotectdatabythehelpof
nologyastheunderlyingissueswhichdemandmorecontrol,
privatehardwareandsoftwareandcanapplywelldeveloped
security,privacy,flexibility,andeaseofuse[12].
cryptologymethods.
Clearly there are beneficial outcomes from the appli-
2.4. Smart Card as Electronic Purse. The original primary
cation of smart cards. Realizing these benefits both for
application of smart cards with microcontrollers was user
individuals and organizations may well profoundly change
identification in the telecommunications sector. In recent
therelationshipbetweenclientsorconsumersandsuppliers
years, however, smart cards have established themselves in
or government bodies. A smart card that is your passport,
anothermarketsector,namely,electronicpaymentsystems.
drivinglicense,creditanddebitcard,andaccesstoyourplace
Duetothelargenumberofcardsinuse,themarketpotential
of work and your car ignition key will undoubtedly alter
of this sector is enormous. Smart cards are by nature par-
relationships due to potential uneasiness about what data
ticularlysuitableforpaymentsystemapplications.Theycan
is held, accessed, and modified [11]. Some of the potential
easilyandsecurelystoredata,andtheirconvenientsizeand
benefits of smart cards are as follows. Using smart cards is
robustnessmakethemeasyforeveryonetouse.Sincesmart
safer than carrying cash for an individual, smart cards can
cards can also actively perform complicated computations
improveaccesstoservicesforthedisabledandelderly,itisa
without being influenced by external factors, it is possible
securemeansofauthenticatingtheidentityofreaderdevice,
to develop totally new approaches to performing payment
it is a portable and secure store of information available to
transactions[3].
all, access can be made available in geographical locations
Theideaofimplementinganelectronicpurseinasmart
whereonlinecommunicationisnotpossible,theopportunity
card goes back to the early days of smart card technology.
of fraud is reduced using smart cards, social disadvantaged
However, only since the mid-1990s has this concept been
groups can gain access to facilities and resources without
realized, since that was when the development of large sys-
feeling stigmatized, and objective selection criteria can be
temsfirstbegan.Electronicpaymentsystemsandelectronic
upheldandtheriskofbiasorfavouritismreduced[11].
purses offer significant benefits to everyone involved. For
Smart cards have a wide range of potential applications
banksandmerchants,theyreducethecostsassociatedwith
and can be utilized for many different purposes. However,
handlingcash.Offlineelectronicpurseslargelyeliminatethe
there are unquestionably areas that are especially suitable
costsofdatatelecommunicationsforpaymenttransactions.
forsmartcards.Theprincipalcharacteristicsofsmartcards
Theriskofrobberyandvandalismisreduced,sinceelectronic
are that they can securely store relatively small amounts of
systems contain no cash to be stolen. For merchants, the
dataandprovideanenvironmentforthesecureexecutionof
fact that transactions are processed more quickly is also a
programs. This makes them excellent candidates for use in
persuasive argument, since it means that cash management
the entire security sector. Another important characteristic
canbeoptimized.Classificationofpaymentcardsande-purse
isthattheyhaveawell-establishedformatthatisconvenient
systems based on smart cards is shown in Figures 2 and 3,
for manual use and handling. Although the smart card
respectively[3].
interfacedoesnotcorrespondtothecurrentPCandInternet
standards, it is still easy to use, which also encourages the
use of smart cards. The best possible uses for smart cards 3.FuzzyAHPMethodology
areapplicationsthatneedalargenumberofinexpensivedata
storagedevicesthatcansecurelystoreindividualorpersonal There has been growth in the number of multiple criteria
dataandthatmustperformsecurity-relatedactivitiessuchas decision-makingmethodsforassistingdecisionmakingdur-
authentication,encryption,and/orsigning[7]. ing the past two decades. These allow decision makers to
Insummary,therangeofsmartcardapplicationsisgrow- evaluatevariousalternativesforachievingtheirgoal[13].
ing for many reasons such as security, multiple application, Analytic hierarchy process (AHP) is a simple decision-
andportability.Smartcardsareusedinmanydifferentappli- making tool to deal with complex, unstructured, and mul-
cationsaroundtheworld,particularlyforelectronicpayment, tiattribute problems [14] or a weight estimation technique
securityandauthentication,transportation,telecommunica- in many areas such as selection, evaluation, planning and
tions, health care, loyalty programs, and education. These development, decision making, and forecasting. The tra-
are some of the more popular application areas [12]. It is ditional AHP requires crisp judgments. However, due to
4 JournalofAppliedMathematics
Let 𝑋 = {𝑥1,𝑥2,...,𝑥𝑛} be an object set, and let 𝑈 =
Electronic purses {𝑢1,𝑢2,...,𝑢𝑚} be a goal set. According to the method of
Chang’sextentanalysis,eachobjectistakenandextentanal-
ysisforeachgoal,𝑔𝑖,isperformed,respectively.Therefore,𝑚
extent analysis values for each object can be obtained, with
thefollowingsigns:
Electronic money Electronic cheque s Prepaid cards
𝑀𝑔1,𝑀𝑔2,...,𝑀𝑔𝑚, 𝑖=1,2,...,𝑛, (1)
Transferrable with restrictions 𝑖 𝑖 𝑖

Completely transferrable where all the 𝑀𝑗 (𝑗 = 1,2,...,𝑚) are triangular fuzzy
𝑔
𝑖
numbers.
The steps of Chang’s extent analysis can be detailed as
Figure3:Classificationofelectronicpursesystemsbasedonsmart
follows[16,18,19,21,25–28].
cards.
Step1. Thevalueoffuzzysyntheticextentwithrespecttothe
𝑖thobjectisdefinedas
thecomplexityanduncertaintyinvolvedinrealworlddeci-
sion problems, a decision maker (DM) may sometimes −1
𝑚 𝑛 𝑚
feel more confident to provide fuzzy judgments than crisp 𝑆 = ∑𝑀𝑗 ⊗[∑∑𝑀𝑗] . (2)
comparisons[15]. 𝑖 𝑔𝑖 𝑔𝑖
𝑗=1 [𝑖=1𝑗=1 ]
The fuzzy analytic hierarchy process (FAHP) is one of
themostpopular[13]ofmethodsthathavebeendeveloped Toobtain ∑𝑚 𝑀𝑗,performthefuzzyadditionoperationof
to handle fuzzy comparison matrices [15, 16]. The FAHP 𝑗=1 𝑔𝑖
𝑚extentanalysisvaluesforaparticularmatrixsuchthat
methodology extends Saaty’s AHP by combining it with
the fuzzy set theory. In the FAHP, fuzzy ratio scales are
𝑚 𝑚 𝑚 𝑚
used to indicate the relative strength of the factors in the ∑𝑀𝑔𝑗 =(∑𝑙𝑗,∑𝑚𝑗,∑𝑢𝑗), (3)
corresponding criteria. Therefore, a fuzzy judgment matrix 𝑖
𝑗=1 𝑗=1 𝑗=1 𝑗=1
can be constructed. The final scores of alternatives are also
represented by fuzzy numbers. The optimum alternative is andtoobtain[∑𝑛 ∑𝑚 𝑀𝑗]−1,performthefuzzyaddition
obtainedbyrankingthefuzzynumbersusingspecialalgebra 𝑖=1 𝑗=1 𝑔𝑖
operators[17].TherearemanyFAHPmethodsproposedby operationof 𝑀𝑔𝑗 (𝑗=1,2,...,𝑚)valuessuchthat
𝑖
variousauthors.Thesemethodsaresystematicapproachesto
𝑛 𝑚 𝑛 𝑛 𝑛
the alternative selection and justification problem by using ∑∑𝑀𝑗 =(∑𝑙,∑𝑚,∑𝑢),
the concepts of fuzzy set theory and hierarchical structure 𝑔𝑖 𝑖 𝑖 𝑖 (4)
𝑖=1𝑗=1 𝑖=1 𝑖=1 𝑖=1
analysis [18, 19]. Decision makers usually find that it is
more confident to give interval judgments than fixed value
andthencomputetheinverseofthevectorin(4)suchthat
judgments. This is because usually he/she is unable to be
explicit about his/her preferences due to the fuzzy nature −1
𝑛 𝑚 1 1 1
of the comparison process [16, 18, 19]. The earliest work in [∑∑𝑀𝑗] =( , , ). (5)
FAHP appeared in van Laarhoven and Pedrycz [20], which 𝑔𝑖 ∑𝑛 𝑢 ∑𝑛 𝑚 ∑𝑛 𝑙
[𝑖=1𝑗=1 ] 𝑖=1 𝑖 𝑖=1 𝑖 𝑖=1 𝑖
compared fuzzy ratios described by triangular membership
functions[18,19,21].Buckley[22]determinesfuzzypriorities Step2. Thedegreeofpossibilityof 𝑀2 =(𝑙2,𝑚2,𝑢2)≥𝑀1 =
ofcomparisonratioswhosemembershipfunctionsaretrape- (𝑙1,𝑚1,𝑢1) isdefinedas
zoidal[18,19,21].Chang(1996)introducesanewapproachfor
handlingfuzzyAHP,withtheuseoftriangularfuzzynumbers 𝑉(𝑀2 ≥𝑀1)=sup[min(𝜇𝑀 (𝑥),𝜇𝑀 (𝑦))] (6)
forpairwisecomparisonscaleoffuzzyAHPandtheuseofthe 𝑦≥𝑥 1 2
extentanalysismethodforthesyntheticextentvaluesofthe
pair-wisecomparisons[18,19].Zhangetal.(2013)proposed andcanbeequivalentlyexpressedasfollows:
amultipleattributedecisionmakingmodeltoseekthenode
importance of complex networks in product research and 𝑉(𝑀2 ≥𝑀1)= hgt(𝑀1∩𝑀2)=𝜇𝑀 (𝑑)
2
development team [23]. W. Zhang and Q. Zhang (2013)
constructedamultistageevaluationcriteriasystemfromthe {{{{1; if𝑚2 ≥𝑚1,
three dimensions of novelty, value, and practicality, each 𝑉(𝑀 ≥𝑀 )= 0; if 𝑙1 ≥𝑢2,
of which is composed of three separate evaluation criteria 2 1 {{{{ 𝑙1−𝑢2 ; otherwise,
system,andthefuzzyAHPmethodisappliedtoobtainthe (𝑚 −𝑢 )−(𝑚 −𝑙 )
{ 2 2 1 1
weightsofeachdimensionandsubdimension[24].
(7)
Inthisstudy,Chang’sextentanalysis[25]isused.Inthe
following,thestepsoftheextentanalysismethodonFAHP where 𝑑 is the ordinate of the highest intersection point 𝐷
aregiven. between𝜇𝑀 and𝜇𝑀 (seeFigure4).
1 2
JournalofAppliedMathematics 5
M2 M1 TheANPgeneralizesawidelyusedmulticriteriadecision
1 making tool, the AHP, by replacing hierarchies with net-
works.TheAHPisawell-knowntechniquethatdecomposes
a problem into several levels in such a way that they form
V(M ≥M)
2 1 a hierarchy. Each element in the hierarchy is supposed to
beindependent,andarelativeratioscaleofmeasurementis
derivedfrompairwisecomparisonsoftheelementsinalevel
ofthehierarchywithrespecttoanelementofthepreceding
level. However, in many cases, there is interdependence
l m l d u m u amongcriteriaandalternatives.TheANPcanbeusedasan
2 2 1 2 1 1
effective tool in those cases where the interactions among
Figure4:Theintersectionbetween𝑀1and𝑀2. theelementsofasystemformanetworkstructure[32].The
processofANPcomprisesfourmajorsteps[31,33,34].
Tocompare𝑀1and𝑀2,boththevaluesof 𝑉(𝑀1 ≥𝑀2) Step 1 (model construction and problem structuring). The
and 𝑉(𝑀2 ≥𝑀1) arerequired.Theintersectionbetween𝑀1 problem should be stated clearly and decomposed into a
and𝑀2isshowninFigure4[18]. rationalsystemlikeanetwork.Thestructurecanbeobtained
bytheopinionofdecisionmakersthroughbrainstormingor
Step3. Thedegreepossibilityforaconvexfuzzynumbertobe otherappropriatemethods.
greaterthan𝑘convexfuzzynumbers𝑀𝑖 (𝑖=1,2,...,𝑘)can
bedefinedby Step 2 (pairwise comparison matrices and priority vectors).
InANP,likeAHP,decisionelementsateachcomponentare
𝑉(𝑀≥𝑀 ,𝑀 ,...,𝑀 ) comparedpairwisewithrespecttotheirimportancetowards
1 2 𝑘
their control criterion, and the components themselves are
=𝑉[(𝑀≥𝑀1) and (𝑀≥𝑀2)and,...,and (𝑀≥𝑀𝑘)] also compared pairwise with respect to their contribution
to the goal. Decision makers are asked to respond to a
=min𝑉(𝑀≥𝑀𝑖), 𝑖=1,2,3,...,𝑘. series of pairwise comparisons where two elements or two
(8) components at a time will be compared in terms of how
they contribute to their particular upper level criterion. In
Assumethat addition,ifthereareinterdependenciesamongelementsofa
component,pairwisecomparisonsalsoneededtobecreated,
𝑑󸀠(𝐴𝑖)=min𝑉(𝑆𝑖 ≥𝑆𝑘). (9) and an eigenvector can be obtained for each element to
show the influence of other elements on it. The relative
For𝑘=1,2,...,𝑛;𝑘≠𝑖.Then,theweightvectorisgivenby importance values are determined on a scale of 1–9 (see
Table11), where a score of 1 represents equal importance
𝑊󸀠 =(𝑑󸀠(𝐴 ),𝑑󸀠(𝐴󸀠),...,𝑑󸀠(𝐴 ))𝑇, (10) between the two elements and a score of 9 indicates the
1 2 𝑛
extremeimportanceofoneelement(rowcomponentinthe
where𝐴𝑖 (𝑖=1,2,...,𝑛)are𝑛elements. matrix)comparedtotheotherone(columncomponentinthe
matrix).
Step4. Vianormalization,thenormalizedweightvectorsare
Areciprocalvalueisassignedtotheinversecomparison;
𝑊=(𝑑(𝐴 ),𝑑(𝐴 ),...,𝑑(𝐴 ))𝑇, (11) thatis,𝑎𝑖𝑗 =1/𝑎𝑗𝑖,where𝑎𝑖𝑗 (𝑎𝑗𝑖)denotestheimportanceof
1 2 𝑛 the𝑖th(𝑗th)elementcomparedtothe𝑗th(𝑖th)element.Like
where𝑊isanonfuzzynumber. AHP,pairwisecomparisoninANPismadeintheframework
of a matrix, and a local priority vector can be derived as
an estimate of the relative importance associated with the
4.AnalyticNetworkProcess(ANP)
elements (or components) being compared by solving the
followingformula:
TheANPisthemostcomprehensiveframeworkforanalysis
of public, governmental, and corporate decisions. It allows
decision makers to include all the factors and tangible or
intangible criteria that have a bearing on making the best 𝐴𝑤=𝜆max.𝑤, (12)
decision[29].
Manydecisionproblemscannotbestructuredhierarchi-
cally because they involve the interaction and dependence
of higher-level elements on lower-level elements [30, 31]. where 𝐴 is the matrix of pairwise comparison, 𝑤 is the
Not only does the importance of the criteria determine the eigenvector, and 𝜆max is the largest eigenvalue of 𝐴. Saaty
importance of the alternatives as in a hierarchy, but also (1980) [35] proposes several algorithms for approximating
theimportanceofthealternativesthemselvesdeterminesthe 𝑤. Thefollowingthree-stepprocedureisusedto synthesize
importanceofthecriteria[30]. priorities[31,33–36].
6 JournalofAppliedMathematics
(1)Sumthevaluesineachcolumnofthepairwisecom- globalprioritiesinasystemwithinterdependentinfluences,
parisonmatrix. the local priority vectors are entered in the appropriate
columns of a matrix, known as a supermatrix. As a result,
(2)Divide each element in a column by the sum of its
a supermatrix is actually a partitioned matrix, where each
respectivecolumn.Theresultantmatrixisreferredto
matrixsegmentrepresentsarelationshipbetweentwonodes
asthenormalizedpairwisecomparisonmatrix.
(components or clusters) in a system [33, 34, 38]. Let the
(3)Sum the elements in each row of the normalized components of a decision system be 𝐶𝑘, 𝑘 = 1,2,...,𝑛,
pthaeirw𝑛iseelecmomenptasriisnonthmeatrroiwx.anThdedsievidfienatlhenusummbebrys whichhas𝑚𝑘elementsdenotedas𝑒𝑘1,𝑒𝑘2,...,𝑒𝑘𝑚𝑘.Thelocal
priorityvectorsobtainedinStep2aregroupedandlocatedin
provide an estimate of the relative priorities for the
appropriatepositionsinasupermatrixbasedontheflowof
elements being compared with respect to its upper
influencefromacomponenttoanothercomponentorfrom
levelcriterion.Priorityvectorsmustbederivedforall a component to itself as in the loop 𝐴 standard form of a
comparisonmatrices.
supermatrixasfollows[34,37]:
Step 3 (supermatrix formation). The supermatrix concept
is similar to the Markov chain process [34, 37]. To obtain
𝑒
11
.
.
.
𝑒 𝐶 ⋅⋅⋅ 𝐶 ⋅⋅⋅ 𝐶
1𝑛1 1 𝐾 𝑁
. 𝑒 ⋅⋅⋅ 𝑒 ⋅⋅⋅ 𝑒 ⋅⋅⋅ 𝑒 ⋅⋅⋅ 𝑒 ⋅⋅⋅ 𝑒
𝐶 .. 11 1𝑛1 𝑘1 𝑘𝑛𝑘 𝑁1 𝑁𝑛𝑁
1
𝑒 𝑊 ⋅⋅⋅ 𝑊 ⋅⋅⋅ 𝑊
𝑊= 𝐶... 𝑘...1 [[[ ...11 ...1𝐾 d ...1𝑁]]] (13)
𝐾 𝑒 [𝑊 ⋅⋅⋅ 𝑊 ⋅⋅⋅ 𝑊 ].
𝐶... 𝑘...𝑛𝑘 [[[ ...𝐾1 𝐾...𝐾 d 𝐾...𝑁]]]
𝑁
𝑒𝑁1 [𝑊𝑁1 ⋅⋅⋅ 𝑊𝑁𝐾 ⋅⋅⋅ 𝑊𝑁𝑁]
.
.
.
𝑒
𝑁𝑛
𝑁
Asanexample,considerthesupermatrixrepresentationofa or between two components. Since there usually is interde-
hierarchywiththreelevels[34,37]: pendence among clusters in a network, the columns of a
supermatrixusuallysumtomorethanone.Thesupermatrix
𝐼 0 0 must be transformed first to make it stochastic; that is,
Wℎ =[w21 0 0], (14) each column of the matrix sums to unity. A recommended
[ 0 W32 𝐼] approach by Saaty (1996) [37] is to determine the relative
importance of the clusters in the supermatrix with the
wherew21 isavectorthatrepresentstheimpactofthegoal columncluster(block)asthecontrollingcomponent[34,38].
on the criteria, W32 is a matrix that represents the impact That is, the row components with nonzero entries for their
of criteria on each of the alternatives, and 𝐼 is the identity blocksinthatcolumnblockarecomparedaccordingtotheir
matrix,andentriesofzeroscorrespondingtothoseelements
impact on the component of that column block [34, 37].
thathavenoinfluence.
With pairwise comparison matrix of the row components
with respect to the column component, an eigenvector can
For the above example, if the criteria are interrelated
beobtained.Thisprocessgivesrisetoaneigenvectorforeach
amongthemselves,anetworkreplacesthehierarchyasshown
in Figure5 [31, 33]. The (2, 2) entry of Wn given by W22 creoslpuemcntivbeloecigke.nFvoercteoarcihscmoulultmipnliebdlobcyka,ltlhtehefiresletmenetnrtysoinftthhee
would indicate the interdependency, and the supermatrix
firstblockofthatcolumn,thesecondbyalltheelementsinthe
wouldbe[34,37]
secondblockofthatcolumn,andsoon.Inthisway,theblock
𝐼 0 0 ineachcolumnofthesupermatrixisweighted,andtheresult
W𝑛 =[w21 W22 0]. (15) is known as the weighted supermatrix, which is stochastic
0 W 𝐼 [34].
[ 32 ]
Raising a matrix to powers gives the long-term relative
Notethatamatrixcanreplaceanyzerointhesupermatrix influences of the elements on each other. To achieve a
ifthereisaninterrelationshipoftheelementsinacomponent convergence on the importance of weights, the weighted
JournalofAppliedMathematics 7
of smart card and payment with smart card. Using e-purse
Goal Goal smart card eliminates cash interchange and provides that
process is made on smaller time and is enrolled, stock is
controlled at workplace, and productivity is increased. In
w w
21 21 additiontointerchangeincompany,thiscardalsocanbeused
asanidentitycardandentrancecard.Fortheintegrationof
W22 this feature, cards must be personalized. Because of all this
Criteria Criteria easeofuse,allprocessesaremadewithonlyonesmartcard
insteadofusingdifferentsmartcardforeachprocess.Finally,
W W variouscharacteristicsthatarenecessaryforacompanyare
32 32
collected in a smart card. The software of these cards is
programmedbyCompanyO.Cardtechnologiesthatprovide
requiredcharacteristicsforprogrammingareobtainedfrom
Alternatives Alternatives
cardcompanies.Therearethreealternatives;AC,TU,andOB
card. These cards are compared according to some criteria
and the best alternative has been selected. MCDM have
(a) (b)
not been used in the case company before; therefore, the
Figure5:Hierarchyandnetwork:(a)ahierarchy;(b)anetwork. selectionshavebeenmadeheuristics.
5.1.Determiningthee-PurseSmartCardTechnologySelection
supermatrix is raised to the power of 2𝑘 + 1, where 𝑘 is an Criteria. In this study, the selection criteria were identified
by decision makers. Thus, an interview was conducted
arbitrarily large number, and this new matrix is called the
with three decision makers who are chosen from different
limitsupermatrix[34,37].Thelimitsupermatrixhasthesame
areassuchasdevelopers,systemanalysts,andacademicians.
formastheweightedsupermatrix,butallthecolumnsofthe
Twelve subcriteria were determined to select the most con-
limitsupermatrixarethesame.Bynormalizingeachblockof
venient e-purse card technology alternative under the four
thissupermatrix,thefinalprioritiesofalltheelementsinthe
main criteria. Also, three potential card technologies were
matrixcanbeobtained[34].
consideredfortheselection.Adetailedquestionnairerelated
withcriteriaandalternativeswaspreparedfortheselection
Step4(selectionofthebestalternatives). Ifthesupermatrix
process.Duringtheidentificationofmainandsubcriteria,the
formed in Step3 covers the whole network, the priority
opinions of experts from Company O were also taken into
weights of alternatives can be found in the column of
account.
alternatives in the normalized supermatrix. On the other
For the three alternative card technologies, criteria are
hand, if a supermatrix only comprises components that are
softwaretechnologyandsoftwareperformance,flexibility,cost,
interrelated, additional calculation must be made to obtain
andservicelevel.Thedefinitionsandsubcriteriaofthemain
theoverallprioritiesofthealternatives.Thealternativewith
criteria are summarized below, and also Table1 shows the
thelargestoverallpriorityshouldbetheoneselected[34].
criteriaandsubcriteria.
Asmentionedbefore,ANPisageneralizationoftheAHP
Software Technology and Software Performance (S). It is the
[33] and based on reasoning, knowledge, and experience
mostimportantcriterionduringtheselectionofsmartcard
of the experts in the field. ANP can act as a valuable aid
forprogrammingofe-pursecardsystems.Itmustbeappro-
for decision making involving both tangible and intangible
priateforsoftwaresecurityandreliability.Performanceand
attributes that are associated with the model under study.
thequickresponsetosoftwarecommandareothersubcriteria
ANPreliesontheprocessofelicitingmanagerialinputs,thus
ofthesoftwaretechnologyandsoftwareperformance.“Soft-
allowing for a structured communication among decision
ware development and easiness of software usage” (SDU),
makers. Thus, it can act as a qualitative tool for strategic
“speed of software working” (SS), “software security and
decision-makingproblems[34].
software credibility” (SSC), and “technical sufficiency” (TS)
aresubcriteriaofthiscriterion.
5.CaseStudy
Flexibility (F). Flexibility of smart card companies can be
In this section, selection of the best e-purse smart card defined as compatible to response customer’s request. This
technology is presented for the case of a company. Firstly, criterioncontainsabilitytosupplyallproductsthatcustomer
e-purse application is explained and then FAHP and ANP has requested and their urgent product demand. “Easily
methods are applied to an e-purse smart card technology supplying of card demands” (ESD), “supplying of urgent
selection problem, respectively. Then, the results of FAHP card demands” (SUD), and “supplying of different sector
and ANP methods are compared with each other. The case demands”(SSD)aresubcriteriaofthiscriterion.
study is about the project of the e-purse application that
is developed by Company O. The proposed model includes Cost(C). Softwarecompaniesengagedwithsmartcardtech-
varioususagefieldsaboute-pursesmartcard:personalization nology want to supply material with minimum price to
8 JournalofAppliedMathematics
Table1:Criteriaandsubcriteriafore-pursesmartcardtechnology Table2:Triangularfuzzynumberoflinguisticterms.
selection.
Linguisticterms Triangularfuzzynumbers
Criteria Subcriteria
Absolutelystrong (7/2,4,9/2)
SDU:softwaredevelopmentandeasinessof
Software Verystrong (5/2,3,7/2)
softwareusage
technology Fairlystrong (3/2,2,5/2)
andsoftware SS:speedofsoftwareworking
Weak (2/3,1,3/2)
performance SSC:softwaresecurityandsoftwarecredibility
Equal (1,1,1)
(S) TS:technicalsufficiency Weak (2/3,1,3/2)
ESD:easilysupplyingofcarddemands Fairlystrong (3/2,2,5/2)
Flexibility(F) SUD:supplyingofurgentcarddemands Verystrong (5/2,3,7/2)
SSD:supplyingofdifferentsectordemands Absolutelystrong (7/2,4,9/2)
AB:appropriatebiddingaccordingtoothercard
Cost(C) firms
PR:pricereductionincomparisonwithother areconvertedintotriangularfuzzynumbersbyusingTable2
cardfirmsaccordingtocardsquantity [39].Followingquestionsaregivenasasampleofquestions
SV:velocityoftechnicalsupportaftersale fromthequestionnaireforthepairwisecomparisonmatrices.
Servicelevel SDS:sufficiencyoftechnicalsupportdepartment Inthequestionnaries,acheckmarkontherightsideof
(SL)
thepreference“equal”meansthatthecriterionontheright
aftersale
OH:onlinetechnicalhelpaftersale side of the preference “equal” is more important than the
one matching on the left side as it is specified by the check
mark.Acheckmarkontheleftsideofthepreference“equal”
Selection of the best e-purse means that the criterion on the left side of the preference
smart card technology “equal”ismoreimportantthantheonematchingontheright
side as it is specified by the check mark [18]. A sample of
S F C SL the questionnaire forms used for comparisons of main and
subcriteriaisgiveninTable3.
With respect to the overall goal “selection of the best
SD SS SSC TS ESD SU SSD AB PR SV SDS OH
e-pursesmartcardtechnology,”considerthefollowing.
Question 1. How important is software technology and soft-
AC card TU card OB card
wareperformance(S)whenitiscomparedwithflexibility(F)?
Figure 6: The hierarchy for selection of e-purse card technology
problem. Question 2. How important is software technology and soft-
wareperformance(S)whenitiscomparedwithcost(C)?
Question 3. How important is software technology and soft-
raise profitability like all production companies. Provider’s wareperformance(S)whenitiscomparedwithservicelevel
moreappropriatepricethantheotherprovidersandhigher (SL)?
discount on the material according to the amount of pur-
chasedmaterialsaresubcriteriaofcost.“Appropriatebidding Question 4. How important is flexibility (F) when it is
according to other card firms” (AB) and “price reduction comparedwithcost(C)?
in comparison with other card firms according to cards
quantity”(PR)aresubcriteriaofthiscriterion. Question 5. How important is flexibility (F) when it is
comparedwithservicelevel(SL)?
ServiceLevel(SL).Qualifiedserviceofproviderisanimpor-
tant factor and it is also significant for provider to be Question6. Howimportantiscost (C)whenitiscompared
consideredashighperformancecompanybythecustomers. withservicelevel(SL)?
“Velocityoftechnicalsupportaftersale”(SV),“sufficiencyof
technical supportdepartmentafter sale”(SDS),and “online Othermatricesaredonewithsamemethod.
technicalhelpaftersale”(OH)aresubcriteriaofthiscriterion.
According to explanations of the aforementioned main
5.3. Numerical Applications of the Methods. In this sec-
and subcriteria, a hierarchical structure for selection of
tion, the best e-purse card technology that will be used
e-pursecardtechnologyisshowninFigure6.
in Company O is selected with FAHP and ANP methods,
respectively. A questionnaire is made in the company to
5.2. Questionnaire. The three of decision makers are asked establish importance weights (fuzzy preference numbers)
to make pairwise comparisons for main and subcriteria thatarenecessaryforselectionofbestcardtechnology.The
mentionedinSection5.1.Aquestionnaireisprovidedtoget questionnairesfacilitatetheansweringofpairwisecompari-
the evaluations. The decision makers’ linguistic preferences sonquestions.
JournalofAppliedMathematics 9
Table3:Asamplefromthequestionnaire.
Selectionofthe
beste-pursesmart Importance(orpreference)ofonecriteriaoveranother
cardtechnology
(3/2,2,5/2) (3/2,2,5/2)
(7/2,4,9/2) (5/2,3,7/2) (2/3,1,3/2) (1,1,1) (2/3,1,3/2) (5/2,3,7/2) (7/2,4,9/2)
Questions Criteria Fairly Fairly Criteria
Absolute Verystrong Weak Equal Weak Verystrong Absolute
strong strong
Q1 S X XX F
Q2 S XX X C
Q3 S X XX SL
Q4 F XXX C
Q5 F XXX SL
Q6 C XXX H
Table4:Evaluationresultsofthecriteriawithrespecttothegoal.
Maincriteria S F C SL
S (1.000,1.000,1.000) (1.500,2.289,2.797) (2.109,2.621,3.130) (1.778,2.289,2.797)
F (0.358,0.437,0.562) (1.000,1.000,1.000) (1.500,2.000,2.500) (0.400,0.500,0.667)
C (0.319,0.382,0.474) (0.400,0.500,0.667) (1.000,1.000,1.000) (0.400,0.500,0.667)
SL (0.358,0.437,0.562) (1.500,2.000,2.500) (1.500,2.000,2.500) (1.000,1.000,1.000)
((1,1,1)⊕(1.500,2.289,2.797)⊕(2.109,2.621,3.130)
5.3.1.ApplyingFAHPtoe-PurseSmartCardTechnologySelec-
tionProblem. Firstly,FAHPmethodisusedforbeste-purse
⊕(1.778,2.289,2.797))
cardtechnologyselection.Inthismethod,thefactors’fuzzy
weights are calculated according to each other for selection
+((0.358,0.437,0.562)⊕(1,1,1)⊕(1.500,2.000,2.500)
of AC, TU, and OB card technologies. For this, criteria
and subcriteria are listed for selecting card technologies.
⊕(0.400⊕0.500⊕0.667))
Fordeterminingtherelativeimportancebetweenmainand
subcriteria,threedecisionmakerswereaskedtorespondfor
+((0.319,0.382,0.474)⊕(0.400,0.500,0.667)
pairwisecomparisons.Accordingtoresultofquestionnaire,
geometricmeanisusedtosetpairwisecomparisons.
⊕(1,1,1)⊕(0.400,0.500,0.667))
Geometric means are obtained as follows. An example
calculationisgiven.
+((0.358,0.437,0.562)⊕(1.500,2.000,2.500)
Theimportanceof“softwaretechnologyandsoftwareper-
formance (S)” is (3/2,2,5/2), (3/2,2,5/2), and (5/2,3,7/2)
⊕(1.500,2.000,2.500)⊕(1,1,1))
whenitiscomparedwith“flexibility(F).”Consider
=(16.122,19.960,23.823)
3 3 5 5 5 7
(√3( × × ),√3(2×2×3),√3( × × )) 𝑆 =(6.387,8.199,9.724)⊗(16.122,19.960,23.823)−1
2 2 2 2 2 2 1
(16)
6.387 8.199 9.724
=(1.500,2.289,2.797). 𝑆 =( , , )
1 23.823 19.960 16.122
𝑆 =(0.268,0.410,0.603).
1
TheevaluationresultsaregiveninTable4.
(17)
Fuzzy synthetic extent values are calculated by using
evaluationresults.Firstly,thevaluesoffuzzysyntheticextents
withrespecttothemaincriteriaarecalculated.Calculationof
𝑆1 isgivenasanexample.Theobtainedvaluesareshownin Importance weights of criteria are calculated by using
fuzzysyntheticvalues.Then,probabilityofpreferenceofone
Table5.Similarcalculationsaredonefortheothermatrices.
to the other is calculated. After this calculation, the weight
Table5depictstheresultsofthecalculations.Consider
vectors are calculated by using the results of probability of
preference. The normalized weight vectors are values that
(1,1,1)⊕(1.500,2.289,2.797)⊕(2.109,2.621,3.130) are used for selection of e-purse smart card technologies.
Tables 6, 7, 8, and 9 are obtained as the priority weights
⊕(1.778,2.289,2.797)=(6.387,8.199,9.724). of the alternatives according to each subcriterion. And the
10 JournalofAppliedMathematics
Table5:Fuzzysyntheticextentvalues.
𝑆 𝑆 𝑆 𝑆
1 2 3 4
(1)Matrix (0.268,0.410,0.603) (0.137,0.197,0.293) (0.089,0.119,0.174) (0.183,0.272,0.407)
(2)Matrix (0.142,0.228,0.344) (0.094,0.142,0.232) (0.237,0.371,0.579) (0.159,0.258,0.426)
(3)Matrix (0.224,0.360,0.602) (0.206,0.331,0.563) (0.197,0.309,0.429)
(4)Matrix (0.430,0.613,0.859) (0.296,0.387,0.518)
(5)Matrix (0.198,0.310,0.488) (0.255,0.413,0.652) (0.264,0.278,0.439)
(6)Matrix (0.396,0.545,0.742) (0.125,0.158,0.209) (0.212,0.297,0.413)
(7)Matrix (0.362,0.515,0.721) (0.131,0.167,0.223) (0.225,0.318,0.450)
(8)Matrix (0.395,0.545,0.826) (0.128,0.163,0.244) (0.135,0.292,0.449)
(9)Matrix (0.207,0.507,0.901) (0.128,0.164,0.279) (0.227,0.328,0.601)
(10)Matrix (0.344,0.519,0.751) (0.164,0.243,0.376) (0.161,0.238,0.365)
(11)Matrix (0.323,0.492,0.721) (0.189,0.279,0.421) (0.160,0.229,0.347)
(12)Matrix (0.359,0.513,0.718) (0.220,0.312,0.439) (0.136,0.176,0.242)
(13)Matrix (0.141,0.151,0.197) (0.501,0.575,0.764) (0.233,0.274,0.372)
(14)Matrix (0.130,0.171,0.247) (0.415,0.569,0.775) (0.180,0.261,0.369)
(15)Matrix (0.430,0.575,0.764) (0.200,0.274,0.372) (0.121,0.151,0.197)
(16)Matrix (0.368,0.545,0.766) (0.222,0.300,0.423) (0.123,0.155,0.215)
(17)Matrix (0.413,0.545,0.753) (0.206,0.293,0.392) (0.123,0.162,0.203)
Table6:Summarycombinationofpriorityweights:subcriteriaofsoftwaretechnologyandsoftwareperformance.
Subcriteria SDU SS SSC TS
Priorityweights 0.199 0.000 0.493 0.308 Alternativepriorityweight
AC 0.940 0.764 0.890 0.537 0.791
Alternatives TU 0.000 0.000 0.000 0.093 0.029
OB 0.060 0.236 0.110 0.370 0.180
Table7:Summarycombinationofpriorityweights:subcriteriaofflexibility.
Subcriteria ESD SUD SSD
Priorityweights 0.368 0.338 0.294 Alternativepriorityweight
AC 0.852 0.714 0.778 0.784
Alternatives TU 0.089 0.089 0.222 0.174
OB 0.059 0.060 0.000 0.042
Table8:Summarycombinationofpriorityweights:subcriteriaofcost.
Subcriteria AB PR
Priorityweights 0.781 0.219 Alternativepriorityweight
AC 0.000 0.000 0.000
Alternatives TU 1.000 1.000 1.000
OB 0.000 0.000 0.000
Table9:Summarycombinationofpriorityweights:subcriteriaofservicelevel.
Subcriteria SV SDS OH
Priorityweights 0.359 0.518 0.123 Alternativepriorityweight
AC 0.500 0.845 1.000 0.740
Alternatives TU 0.500 0.155 0.000 0.260
OB 0.000 0.000 0.000 0.000