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DOI: 10.15240/ ul/001/2016-2-014
In oduc ion
The ask o he p esen pape is o ou line
a o malized quali a i e model (FQM) o online
us (OT). OT is i al o es ablishing and
main aining comme cial ela ionships on he
in e ne (G abne -K aeu e , 2002; Van De
Heijden e al., 2003; Kim e al., 2008; 2012;
Beldad e al., 2010; Delina & D áb, 2010).
T us is especially impo an when he e is
ela i e lack o ce ain y, o mal ules, cus oms
and ag eemen s (B adach e al., 1989; Ge en
& S aub, 2004), as is o en he case wi h
e-comme ce in e ac ion and online in e ac ion
in gene al (Ge en, 2000; McKnigh e al., 2002;
Ge en & S aub, 2004).
OT is a mul idimensional p oblem
(McKnigh & Che any, 2001; McKnigh e al.,
2002; Shanka e al., 2002; Chau e al., 2007;
Beldad e al., 2010). FQMs a e well sui ed o
ackling mul idimensional asks. Also, FQMs
a e use ul whene e ague and/o quali a i e
in o ma ion need o be included in o a model.
In he OT con ex i migh be necessa y o
conside o ins ance he in l uence o pe cei ed
social p esence embedded in a web si e (Ge en
& S aub, 2004; Cy e al., 2007; Hassanein &
Head, 2007) o posi i e wo d o mou h (G abne -
K aeu e , 2002; Co bi e al., 2003; U z e
al., 2012). I migh be di i cul o p ohibi i ely
cos ly o measu e hese in l uences p ecisely
o quickly enough (e.g. when online companies
need o mee deadlines o s a egic decisions).
I is app op ia e o use an FQM hen.
FQMs cap u e ela ionships among
a iables in he o m o deg aded (simpli i ed)
equa ions and s a is ical ela ions and/o in
he o m o common-sense heu is ics (e.g.
i X goes up, Y goes down wi h inc easing
apidi y). Quali a i e me hodology (Kuipe s,
1989; Dohnal, 1991; T a e-Massuyes e al.,
2004) has been used in some o m o model o
example in es men decisions and economic
p oblems (Bena och & Dha , 1995; Hinkkanen
e al., 2003; Cu ic e al., 2008; Konečný e al.,
2010; Kocmano á e al., 2011) and a a ie y
o enginee ing p oblems. See Bou seau e al.
(1995), De Jong (2004) and P ice e al. (2006)
o an o e iew.
Quali a i e models cap u e he undamen al
ea u es o a sys em unde s udy, while
elimina ing quan i a i e de ail (Kuipe s, 1989).
Quali a i e modeling can be seen as one o
he “unce ain y calculi”, such as uzzy se s
(Zadeh, 1965; Dubois & P ade, 1991; Hub &
Za loukal, 2009), ough se s (Pawlak, 1982)
and o de o magni ude easoning (Raiman,
1991). Such calculi can be help ul when dealing
wi h online us (Song e al., 2005; Chak abo y
& Chak abo y, 2007; Li e al., 2009; Li e al.,
2012), especially unde in o ma ion sho age,
measu emen di i cul ies, ime p essu e o
make decisions and/o unce ain y, o when
se e al no el, subjec i e and/o di i cul o
measu e (e.g. quali a i e only) a iables a e
being conside ed.
We p opose a gene al me hodological
amewo k ha enables inco po a ion o many
e en e y ague and e y di e se in l uences on
OT in he con ex o e-comme ce.
Al hough he speci i c e sion o he
quali a i e algo i hm o iginally p oposed by
he second au ho has been used se e al
imes in he pas , mos ecen ly in Vícha &
Dohnal (2008a, 2008b), Konečný e al. (2010),
Kocmano á e al. (2011), Režňáko á e al.
(2012), his is ac ually he i s pape whe e one
o he p incipal aspec s o he algo i hm, namely
selec ion o a consis en se o scena ios, is
ea ed explici ly and in de ail (see sec ion 1.2).
1. Me hod
1.1 Quali a i e Models
The e a e only h ee quali a i e alues:
posi i e, ze o and nega i e. The symbols used
FORMALIZED QUALITATIVE MODELING
OF ONLINE TRUST: INTRODUCTION
OF THE METHOD AND A DETAILED EXAMPLE
Š ěpán Veselý, Mi ko Dohnal
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a e +, 0, -, espec i ely. A quali a i e scena io
o a quali a i e model is speci i ed i all i s n
quali a i e a iables X  (X1, X2, …, Xn) a e
desc ibed by he quali a i e iple s (X, DX,
DDX), whe e DX and DDX a e he i s and
second quali a i e de i a i es wi h espec o
ime (o an independen a iable in gene al).
Le us suppose ha he iple (++0)  (T,
DT, DDT) ep esen s isk a e sion R( ) as
a unc ion o ime: i means ha isk a e sion is
posi i e (R = +), i is inc easing in his example
(DR = +) and he inc ease is linea (DDR = 0) as
he second de i a i e is ze o.
In o mally speaking, he i s quali a-
i e de i a i e ells us whe he a a iable is
inc easing, dec easing, o s able as a unc ion o
ano he a iable – he i s quali a i e de i a i e
is posi i e, nega i e, and ze o in hese cases,
espec i ely. Again in o mally speaking, he
second quali a i e de i a i e ells us whe he
such a change (i.e. inc ease o dec ease) in
a a iable is accele a ing, s able o decele a ing
– he second quali a i e de i a i e is posi i e,
ze o, and nega i e in hese cases, espec i ely.
Looking a Fig. 1 on he nex page, in
pic u es 21, 22 and 23 a e ins ances o unc ions
wi h posi i e i s quali a i e de i a i e, while in
pic u es 24, 25 and 26 we can see ins ances
o unc ions wi h nega i e i s quali a i e
de i a i e. A unc ion wi h he i s quali a i e
de i a i e equal o ze o would be ep esen ed by
a ho izon al s aigh line (pa allel wi h he X axis).
Pic u es 22 and 25 in Fig. 1 gi e examples
o unc ions wi h he second quali a i e
de i a i e equal o ze o. Pic u es 21 and
26 ep esen unc ions wi h posi i e second
quali a i e de i a i e ( he inc ease o dec ease
in Y is becoming mo e and mo e p onounced
as a unc ion o X), while pic u es 23 and 24
ep esen unc ions wi h nega i e second
quali a i e de i a i e (we can see ha he
inc ease o dec ease in Y wi h espec o he
inc ease in X g adually l a ens ou ).
A ypical example o a quali a i e knowledge
i em can be o malized by a ce ain simple
ela ion be ween wo a iables X and Y. Fo
example:
I he p ice X o a p oduc
is dec easing hen he demand
Y is inc easing.
(1)
A o mal in e p e a ion o he quali a i e
knowledge i em (1) is DY/DX = -, whe e DY/DX
is he i s quali a i e de i a i e o Y wi h espec
o X (in his example he de i a i e is nega i e).
Typical examples o quali a i e ela ions a e
gi en in Fig. 1.
The iden i i ca ion numbe s gi en in Fig. 1
a e shape codes o he espec i e quali a i e
shapes, i.e. o ins ance 21 is a code numbe
o unc ion cha ac e ized by posi i e alue
o Y and posi i e i s and second quali a i e
de i a i es o Y wi h espec o X ( iple +++).
The iden i i ca ion numbe s a e employed in
sec ion 2.1.
I he second de i a i e is no known
hen he e a e wo a ian s o quali a i e
p opo ionali y:
M_+ I X is inc easing hen Y is inc easing.
I X is dec easing hen Y is dec easing. (2)
M_- I X is inc easing hen Y is dec easing.
I X is dec easing hen Y is inc easing. (3)
Fo mo e de ails see e.g. Kuipe s (1989),
Pa sons and Dohnal (1995), T a e-Massuyes
e al. (2004).
A key concep in he app oach o quali a i e
modeling p esen ed he e is “quali a i e
scena io” o simply “scena io”.
In plain wo ds, a scena io ep esen s
a concise quali a i e desc ip ion e.g. o an
objec o a sys em. An example o a scena io
could be: I p ice o p oduc X inc eases, we will
sell less X. Ano he example could be: I p ice
o X is s able and i X’s epu a ion o quali y
inc eases, we will sell mo e X. These wo
examples desc ibe a business de elopmen
using wo (p ice and sales) and h ee (p ice,
sales and epu a ion o quali y) a iables,
espec i ely.
Technically, a scena io consis s o a se ies
o a iables. Each a iable in he scena io is
quali a i ely desc ibed by i s s a e (posi i e
quan i y, nega i e quan i y, ze o quan i y) and
by he i s and second quali a i e de i a i es
(usually wi h espec o ime). As we al eady
s a ed a he beginning o his sec ion, hese
h ee quali ies each a iable can ake can ha e
only h ee possible alues (+, - and 0). The h ee
quali ies each a iable can ake can he e o e
be desc ibed by a sequence o h ee signs, i.e.
a iple , as was also al eady men ioned abo e.
To illus a e how a scena io is desc ibed
using iple s, le us e u n o he example o
a quali a i e scena io men ioned p e iously:
“I p ice o X is s able and i X’s epu a ion
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o quali y inc eases [le us assume ha i
inc eases linea ly, so he second quali a i e
de i a i e is ze o], we will sell mo e X [le us
assume ha he inc ease in sales is slowing
down because o g adual demand sa u a ion, so
he second quali a i e de i a i e is nega i e].”
This scena io can be desc ibed by he ollowing
se ies o iple s: +00 (p ice), ++0 ( epu a ion),
++- (sales). Each scena io can be con enien ly
displayed in one ow o a able whe e each cell
con ains quali a i e desc ip ion o one a iable/
one iple (see Tab. 2 in sec ion 2.3).
As we will show nex , some scena ios
ep esen possible solu ions o a quali a i e
model because hey a e consis en wi h a se
o cons ain s based on a ailable knowledge
abou a p oblem (e.g. abou online us and
i s de e minan s), while o he scena ios a e
disca ded because hey a e no consis en wi h
he se o cons ain s (see sec ion 1.2). Those
disca ded scena ios ypically include ce ain
ela ions be ween a iables ha a e deemed
unlikely o impossible based on he a ailable
knowledge ( o example a nega i e ela ion
be ween he le el o us owa ds an online
si e and his si e’s pe cei ed quali y and ease
o use).
1.2 Quali a i e Vec o Op imiza ion
Le us suppose ha he e a e wo independen
a iables X1, X2 and wo objec i e unc ions Q1,
Q2. The e is a ec o F o cons ain s ep esen ed
Fig. 1: Examples o pai -wise quali a i e equa ionless ela ions
Sou ce: own
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by a se o equa ionless ela ions among (some
o all) o he a iables X1, X2, Q1, Q2:
F(X1, X2, Q1, Q2) = 0 (4)
Such a se o cons ain s (4) cons i u es
he quali a i e model o he p oblem a hand.
A gi en model can ha e any numbe o
independen a iables and objec i e unc ions.
A conc e e example o a quali a i e model (i.e.
a se o cons ain s) desc ibing he p oblem o
online us is gi en in (6) in sec ion 2.2. Ano he
e y simple example o a cons ain is gi en in
(5) in his sec ion. The cons ain (5) consis s o
a single ela ion (namely he nega i e quali a i e
p opo ionali y) be ween wo a iables, X and Y.
This e y simple model (5) will be used o
illus a e how he cons ain s a e employed o
di e en ia e solu ions o a p oblem ha a e
consis en and solu ions ha a e inconsis en
wi h a model o a p oblem. In simple wo ds we
can say ha solu ions consis en wi h he model
can happen, while inconsis en solu ions can
no ake place in eali y (as a as he knowledge
used o cons uc he model is alid, o cou se).
A gi en model (i.e. he se o cons ain s) can be
based on empi ical obse a ion, on p e iously
published esul s o on expe opinions.
The p esen quali a i e algo i hm is based
on sys ema ic con on a ion o all possible
iple s o each a iable and he model i sel .
Scena ios (solu ions) consis en wi h he model
(i.e. wi h he se o cons ain s) a e selec ed,
while inconsis en scena ios a e ejec ed. This
ype o solu ion is called b u al o ce in a i i cial
in elligence.
We ha e now desc ibed, in gene al
e ms, how a quali a i e model is sol ed.
To ecapi ula e: he possible solu ions (i.e.
scena ios) a e selec ed i hey a e consis en
wi h a se o cons ain s o med by a se o
quali a i e ela ions be ween a iables (such as
(5) and (6) below). In he ollowing pa ag aphs,
we desc ibe he p ocess o sol ing a quali a i e
model in mo e de ail. Reade s in e es ed
mainly in he applica ion o quali a i e modeling
o online us can now skip di ec ly o sec ion 2.
As we al eady unde s and on he concep ual
le el, scena ios selec ion can be seen as
a consis ency p oblem. A he beginning o
he p ocess o model de elopmen we usually
ha e jus a se o a iables. E en a his ini ial
s age i is possible o calcula e solu ions o he
quali a i e model. Bu i would no ha e any
p ac ical alue, because we would ob ain all
“imaginable” scena ios, i.e. all combina ions o
quali a i e alues o each iple .
Recall ha in a scena io each a iable
is ep esen ed by a quali a i e iple (X, DX,
DDX) – see sec ion 1.1. In he p esen model o
online us we ha e 13 a iables (see sec ion
2.1), hence 13 iple s in each scena io. Each
alue (X, DX and DDX) in he iple can be
ei he +, -, o 0. So, a his ini ial s age, he e
a e 33 = 27 possible combina ions o each
iple . Since we ha e 13 such iple s (one o
each a iable) in each scena io, he e a e 2713
possible combina ions o +, -, and 0, whe e
each combina ion ep esen s one “imaginable”
scena io.
This as numbe o 2713 scena ios needs o
be educed o ob ain a p ac ical solu ion. This is
done by including new knowledge in he model.
Be o e we show how he numbe o
scena ios is educed o he online us model
(see Tab. 3 in sec ion 2.3), we will ou line he
basic p inciple o how inconsis en scena ios
a e disca ded om he model wi h he inclusion
o knowledge i ems.
Conside he ollowing simple example. The
in e ela ion
M_- X Y (5)
s a es he e is a nega i e ela ionship be ween
a iables X and Y. All scena ios ha iola e his
ela ionship mus be disca ded om he model
when his knowledge i em is en e ed. I we
had a model wi h jus wo a iables (X and Y),
he model solu ion be o e and a e en e ing
in e ela ion (5) would look as shown in Tab. 1.
The solu ion in Tab. 1 is in ui i ely
comp ehensible: we mus simply exclude
all scena ios ha ha e o he alues o i s
de i a i es (DX) han ei he “+” o X and “-“ o
Y o “-“ o X and “+” o Y. To see his, le us
say ha X is inc easing as a unc ion o some
a iable Z (e.g. ime). This means ha he
i s quali a i e de i a i e o X wi h espec o
Z is posi i e. I du ing he same change in Z
(e.g. ime) Y also inc eased, i.e. DY = + (wi h
espec o Z), his would mean ha X and Y
mo ed in he same di ec ion (bo h inc eased as
a unc ion o Z). This is ep esen ed by scena io
1 in Tab. 1. Howe e , such a de elopmen is
no possible gi en cons ain (5) which equi es
a nega i e p opo ionali y be ween X and Y,
i.e. when X goes up, Y mus go down and ice
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e sa. Consequen ly, only scena ios 5 and 7 in
Tab. 1 a e consis en wi h cons ain (5).
In con as , scena ios 1 and 2 (in Tab. 1)
would be consis en wi h a cons ain s ipula ing
a posi i e p opo ionali y be ween he a iables.
Scena ios 4, 6, 8 and 9 indica e he e is no
ela ion be ween he a iables (when one
a iable changes in ei he di ec ion, he e is no
change in he emaining a iable). Scena io 3
desc ibes a si ua ion whe e he e a e no
changes in ei he a iable, hus i canno be
shown ha he e ac ually is a posi i e ela ion
be ween X and Y as equi ed by (5). Scena io 3
is he e o e also disca ded om he se o
solu ions consis en wi h cons ain (5).
2. Resul s and Discussion
2.1 Model Va iables
OT can be cha ac e ized by he ollowing se o
13 a iables, 11 independen a iables and wo
objec i e unc ions:
Objec i e unc ions:
TRU Le el o us owa ds an online si e/
company
RIS Pe cei ed isk o in e ac ion wi h he
si e/company (Ho man e al., 1999;
Yoon, 2002; Lacohee e al., 2006; Kim
e al., 2008)
Independen a iables:
FAM Familia i y wi h he si e/company
(Ge en, 2000; Ge en & S aub, 2004)
MAR Le el o he online company’s
ma ke o ien a ion, e.g. se ices
cus omiza ion (S ini asan e al., 2002;
Co bi e al., 2003; Koehn, 2003)
SIT Pe cei ed websi e quali y and ease
o use (McKnigh & Che any, 2001;
G abne -K aeu e , 2002; Liao e al.,
2006; Chau e al., 2007; Kim e al.,
2008, 2012)
SOC Social p esence embedded in he web
si e (Ge en & S aub, 2004; Cy e al.,
2007; Hassanein & Head, 2007)
BEN Pe cei ed bene olence o he online
company (McKnigh e al., 2002;
Ge en & S aub, 2004)
REP Si e’s/company’s posi i e epu a ion
(McKnigh & Che any, 2001; Casalo
e al., 2008; Kim e al., 2008)
WOM Le el o posi i e o wo d o mou h
(G abne -K aeu e , 2002; Co bi e
al., 2003; Lacohee e al., 2006)
PAR Si e’s/company’s pa ne ship wi h
well known pa ne s (Co bi e al.,
2003; Zhang, 2004; Kim e al., 2008;
Hong & Cho, 2011)
EXP Use ’s web expe ience (McKnigh e
al., 2002; Co bi e al., 2003; Lacohee
e al., 2006; Me zge , 2006; Li e al.,
2009)
Model be o e en e ing in e ela ion (5) Model a e en e ing in e ela ion (5)
Va iables Va iables
Scena io X Y Scena io X Y
1 ++* ++*
2 +-* +-*
3 +0* +0*
4 ++* +0*
5 +-* ++* 5 +-* ++*
6 +0* +-*
7 ++* +-* 7 ++* +-*
8 +-* +0*
9 +0* ++*
No e: All a iables a e assumed o be posi i e. Fo simplici y, second de i a i es a e no conside ed in his example,
hus he second de i a i e (DDX) is deno ed by * in all iple s (* can mean ei he +, - o 0).
Sou ce: own
Tab. 1: Scena ios be o e and a e en e ing an in e ela ion
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PRE Numbe o he use ’s p e ious posi i e
expe iences wi h online in e ac ion
(Ge en & S aub, 2004; Fla ian e al.,
2006; Casalo e al., 2008)
TEC Pe cei ed echnological us wo hi-
ness o he si e/company (G abne -
K aeu e , 2002; Co bi e al., 2003;
Lacohee e al., 2006)
2.2 Model Ins uc ions
The ollowing se (6) o pai -wise quali a i e
ela ions is used o o malize ela ions among
he se o a iables om sec ion 2.1. The se o
in e ela ions is inspi ed by many dialogues wi h
a eam o expe s and a g oup o in e ne use s
and by s udies quo ed abo e in sec ion 2.1. The
expe s we e MBA s uden s a B no Uni e si y
o Technology wi h subs an ial expe ience in
online ade and/o ma ke ing. The in e ne
use s we e selec ed p e-g adua e s uden s a
B no Uni e si y o Technology. The quali a i e
model is ep esen ed by he ollowing se o
ela ions (see Fig. 1):
No. Shape X Y (see Fig. 1)
1 23 WOM FAM
2 M_+ (see (2)) SIT MAR
3 M_+ REP MAR
4 21 WOM MAR
5 21 WOM SIT
6 21 TEC SIT
7 21 BEN SOC
8 M_+ REP BEN
9 M_+ WOM BEN
10 23 PAR BEN
11 23 PRE BEN
12 M_+ TEC BEN
13 23 WOM REP
14 M_+ TEC REP
15 M_+ TEC EXP
16 26 RIS TRU
17 23 FAM TRU
18 23 MAR TRU
19 23 SIT TRU
20 23 SOC TRU
21 23 BEN TRU
22 23 REP TRU
23 23 PAR TRU
24 M_+ PRE TRU
25 24 FAM RIS
26 24 SIT RIS
27 M_- BEN RIS
28 24 REP RIS
29 24 PAR RIS
30 24 EXP RIS
31 M_- PRE RIS
32 24 TEC RIS
(6)
2.3 Model Resul s – Scena ios
The se o 23 scena ios – see Tab. 2 – is
gene a ed using so wa e employed in Vícha
and Dohnal (2008a; 2008b). The so wa e was
p og ammed by a g oup a ound he second
au ho . As a as we know, he e a e cu en ly no
widesp ead comme cial so wa es o analyzing
quali a i e p oblems and di e en esea ch
g oups o en use hei own so wa es. Howe e ,
analy ical ools o quali a i e compu a ions can
be p og ammed o example in MATLAB.
Di e en quali a i e p oblems ela ed o
online us can be easily sol ed using he se o
scena ios in Tab. 2 which ep esen a comple e
desc ip ion o all possible beha io s wi hin
he modeled sys em (cons ained by ela ions
gi en in (6)).
All a iables in Tab. 2 a e posi i e because
o hei e y na u e. The e o e he i s alues
in all iple s (in Tab. 2) a e always equal o
+. Fo example scena io 12 is a s eady s a e
si ua ion: all i s and second de i a i es a e
ze os. The e o e no hing is happening, he e
a e no changes in ime.
Scena ios 1–10 indica e e.g. ha le el o
us owa ds he company (TRU) inc eases
as a unc ion o ime and pe cei ed isk o
in e ac ion wi h he si e/company (RIS)
dec eases as a unc ion o ime, while he es
o he a iables go up. Scena ios 14–23 gi e he
opposi e. Tha means all independen a iables
in he p esen model a e posi i ely linked o
TRU and nega i ely linked o RIS ( his is no
su p ising, e.g. in Kim and Pa k (2013) six ou
o se en independen a iables we e posi i ely
ela ed o online us ). The e a e, howe e ,
some di e ences in he p ecise cha ac e o he
inc ease/decline o he a iables wi h espec o
he second de i a i es. Fo example in scena io
1 all a iables inc ease (o in he case o RIS
dec ease) mo e and mo e quickly (all iple s a e
equal o +++ and +--, espec i ely), whe eas in
scena io 10 all a iables inc ease (o in he case
o RIS dec ease) wi h a dec easing apidi y (all
iple s a e equal o ++- and +-+, espec i ely).
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The na u e o one o he objec i e unc ions
(TRU) equi es maximiza ion, whe eas he o he
objec i e unc ion (RIS) equi es minimiza ion,
hence, he e a e 10 ela i ely a o able
scena ios, i.e. scena ios 1–10, and 10 ela i ely
undesi able ones, scena ios 14–23.
Le us o example suppose ha an online
company is unce ain abou he e ec an inc ease
in he a iable “social p esence embedded in
he web si e” (SOC) will ha e on “pe cei ed
isk o in e ac ion wi h he si e/company”
(RIS). Ha ing a look a scena ios 1–10 (and
columns RIS and SOC) in Tab. 2 would ell he
company manage s ha he e ec ough o be
posi i e. Also, i seems ha he e ec would be
almos always he same (wi h he excep ion o
scena io 1) i espec i e o he speed wi h which
he changes in SOC a e implemen ed.
We need o keep in mind, hough, ha FQMs
a e in o ma ion non-in ensi e. This implies ha
hey usually cap u e only he mos obus aspec s
o he desc ibed sys ems. This is he case
especially when he solu ions a e na owed down
o jus a ew scena ios (i.e. when he amoun o
a ailable quali a i e knowledge is la ge, see Tab.
3 and ex below). Mo e in o ma ion in ensi e
me hods (e.g. uzzy ma hema ical me hods o
s a is ics) can be subsequen ly used o gain
addi ional insigh s in o he s udied sys ems/
p oblems. Howe e , his is no always an op ion in
high-speed en i onmen s, o example because
collec ion o quan i a i e da a akes ime.
Scena io Va iables (see sec ion 2.1)
TRU RIS FAM MAR SIT SOC BEN REP WOM PAR EXP PRE TEC
1 +++ +-- +++ +++ +++ +++ +++ +++ +++ +++ +++ +++ +++
2 ++- +-+ ++- ++- ++- +++ ++- ++- ++- +++ ++- ++- ++-
3 ++- +-+ ++- ++- ++- +++ ++- ++- ++- ++0 ++- ++- ++-
4 ++- +-+ ++- ++- ++- +++ ++- ++- ++- ++- ++- ++- ++-
5 ++- +-+ ++- ++- ++- ++0 ++- ++- ++- +++ ++- ++- ++-
6 ++- +-+ ++- ++- ++- ++0 ++- ++- ++- ++0 ++- ++- ++-
7 ++- +-+ ++- ++- ++- ++0 ++- ++- ++- ++- ++- ++- ++-
8 ++- +-+ ++- ++- ++- ++- ++- ++- ++- +++ ++- ++- ++-
9 ++- +-+ ++- ++- ++- ++- ++- ++- ++- ++0 ++- ++- ++-
10 ++- +-+ ++- ++- ++- ++- ++- ++- ++- ++- ++- ++- ++-
11 +0+ +0- +0+ +0+ +0+ +0+ +0+ +0+ +0+ +0+ +0+ +0+ +0+
12 +00 +00 +00 +00 +00 +00 +00 +00 +00 +00 +00 +00 +00
13 +0- +0+ +0- +0- +0- +0- +0- +0- +0- +0- +0- +0- +0-
14 +-+ ++- +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+
15 +-- +++ +-- +-- +-- +-+ +-- +-- +-- +-+ +-- +-- +--
16 +-- +++ +-- +-- +-- +-+ +-- +-- +-- +-0 +-- +-- +--
17 +-- +++ +-- +-- +-- +-+ +-- +-- +-- +-- +-- +-- +--
18 +-- +++ +-- +-- +-- +-0 +-- +-- +-- +-+ +-- +-- +--
19 +-- +++ +-- +-- +-- +-0 +-- +-- +-- +-0 +-- +-- +--
20 +-- +++ +-- +-- +-- +-0 +-- +-- +-- +-- +-- +-- +--
21 +-- +++ +-- +-- +-- +-- +-- +-- +-- +-+ +-- +-- +--
22 +-- +++ +-- +-- +-- +-- +-- +-- +-- +-0 +-- +-- +--
23 +-- +++ +-- +-- +-- +-- +-- +-- +-- +-- +-- +-- +--
Sou ce: Au ho s
Tab. 2: Online us scena ios
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We can say ha he p esen model is well
speci i ed by in e ela ions gi en in (6), which
causes i o be qui e es ic i e, i.e. he e is li le
a iabili y in he scena ios ob ained. I less inpu
knowledge (such as (6)) was a ailable, he model
would be less well speci i ed and consequen ly
less es ic i e, and mo e a iabili y would be
encoun e ed in he scena ios ob ained (e.g.
ce ain a iables would be linked o ce ain o he
a iables posi i ely in a gi en subse o scena ios
and nega i ely in ano he subse ).
Relying on a es ic i e model has a po en ial
disad an age in ha ce ain sub le ela ions o
di e ences may be dis ega ded in he model in
o de o ob ain he se o he mos obus o mos
ypical scena ios (e.g. in he p esen model we
igno e he possibili y ha he ela ion be ween
SIT and TRU migh be pa ially cul u e-sensi i e,
see Pa k e al., 2012). On he o he hand, i is
also possible o de elop an ad hoc quali a i e
model “ ypical” o an unusual si ua ion/sys em.
Table 3 displays he numbe o online us
scena ios ob ained using he basic p inciple
o consis ency ou lined in sec ion 1.2. The
columns “In e ela ions en e ed” gi e he ange
o in e ela ions en e ed (i.e. 1–3 means ha
in e ela ions 1, 2 and 3 om (6) ha e been
en e ed in o he model).
Using he p inciple o consis ency, he as
numbe o “imaginable” scena ios (2713) has
been apidly educed by en e ing a ailable
pieces o knowledge.
As is appa en om Tab. 3 he solu ions o
quali a i e models become in e p e able a e
including abou 25 pai -wise in e ela ions
be ween a iables. This s a emen is ue
o models wi h abou he same numbe o
a iables we ha e in ou model o online us .
Mo e (less) knowledge i ems need o be en e ed
i he model ea u es mo e (less) a iables.
I can also be obse ed ha en e ing ce ain
in e ela ions (e.g. in e ela ions numbe 5, 13,
14, 18, 26 – see Tab. 3) does no educe he
numbe o scena ios ob ained. The eason is
ha he espec i e se o scena ios be o e he
pa icula in e ela ion was en e ed had al eady
been consis en wi h ha in e ela ion.
FQM de elopmen is a mul i-s ep p ocess,
and he p esen model can be modi i ed/
upg aded o add ess speci i c p ac ical and
In e ela ions en e ed Numbe o scena ios In e ela ions en e ed Numbe o scena ios
None 2713 1-16 819
All a iables posi i e* 913 1-17 187
1 407953774917 1-18 187
1-2 45328197213 1-19 187
1-3 5036466357 1-20 187
1-4 731794257 1-21 187
1-5 731794257 1-22 187
1-6 176969853 1-23 187
1-7 28402569 1-24 59
1-8 2421009 1-25 23
1-9 1594323 1-26 23
1-10 255879 1-27 23
1-11 54675 1-28 23
1-12 45927 1-29 23
1-13 45927 1-30 23
1-14 45927 1-31 23
1-15 5103 1-32 23
No e: * We assume ha all a iables a e posi i e la e on (in his able) as well.
Sou ce: own
Tab. 3: Numbe o scena ios dependen on he pai -wise ela ions en e ed in he model
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heo e ical needs. Also, i is possible o
calcula e all possible ansi ions be ween he
quali a i e scena ios (Režňáko á e al., 2012).
The possibili y o upda e quali a i e models
quickly and easily based on an in l ow o new
quali a i e in o ma ion can be an ad an age in
u bulen en i onmen s such as elec onic e ail
ma ke s o he compu e and mobile phones
indus ies.
The ob ious limi a ion o FQM is ha
quali a i e easoning can answe quali a i e
que ies only, no quan i a i e ones, and hus
can se e jus as a complemen o he exis ing
quan i a i e me hods (and/o as a igo ous
o maliza ion o quali a i e me hods, such
as case s udies). Howe e , inclusion o
ma hema ical equa ions in o quali a i e models
is possible (Vícha & Dohnal, 2008a; 2008b).
FQMs can en ich he me hodological
ins umen a ium used in he s udy o OT (e.g.
G abne -K au e & Kaluscha (2003) ad oca e
he use o a b oad spec um o esea ch ools).
The main ad an ages o FQMs a e:
 No nume ical alues o cons an s and
pa ame e s a e needed (i.e. in o ma ion
non-in ensi e).
 The se o possible solu ions (scena ios)
is comple e, i.e. he e canno be any o he
quali a i e scena ios ha a e no gene a ed
by he quali a i e model.
 FQMs a e l exible, di e se a iables can be
included.
 They a e inexpensi e and eadily
unde s andable by p ac i ione s.
Conclusion
Quali a i e app oach has much o o e when
highly complex and/o pa ially ague p oblems
such as OT a e examined. In he p esen
s udy o OT de e minan s a o mal ool o
dealing wi h da a o non-nume ical na u e was
employed o gene a e a FQM consis ing o
23 possible scena ios. The model ob ained is
de i ni ely no he only possible al e na i e. Many
modi i ca ions, upg ades and ex ensions a e
possible. The pape p esen s jus me hodology
and a simple model as a demons a ion.
Also, his is he i s pape whe e one o he
p incipal aspec s o he p esen quali a i e
algo i hm, namely selec ion o a consis en se
o scena ios, is ea ed explici ly and in de ail.
FQMs can complemen es ablished ools o
OT analysis wi h e y li le addi ional cos . This
migh be p o i able especially unde in o ma ion
sho age, measu emen di i cul ies, ime
p essu e o make decisions and/o unce ain y,
o when se e al no el, subjec i e and/o di i cul
o measu e (e.g. quali a i e only) a iables a e
conside ed when dealing wi h online us in he
e-comme ce con ex .
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