146 2021, XXIV, 1
Finance
DOI: 10.15240/ ul/001/2021-1-010
ALTMAN MODEL VERIFICATION USING
A MULTI-CRITERIA APPROACH FOR
SLOVAKIAN AGRICULTURAL ENTERPRISES
Roman Va ek1, Pe a Gundo á2, I ana K a čáko á Vozá o á3,
Ras isla Ko ulič4
1 Technical Uni e si y o Libe ec, Facul y o Economics, Depa men o In o ma ics, Czech Republic, ORCID:
0000-0002-6047-9434, [email p o ec ed];
2 Ma ej Bel Uni e si y in Banská Bys ica, Facul y o Economics, Depa men o Co po a e Economics and
Managemen , Slo akia, ORCID: 0000-0003-2335-0073, [email p o ec ed];
3 Uni e si y o P ešo , Facul y o Managemen , Depa men o Economics and Economy, Slo akia, ORCID:
0000-0002-3056-5294, [email p o ec ed];
4 Uni e si y o P ešo , Facul y o Managemen , Depa men o Economics and Economy, Slo akia, ORCID:
0000-0002-8341-3016, as isla [email p o ec ed].
Abs ac : The Al man model is s ill one o he mos widely used p edic i e models in he 21s
cen u y, and i aims o highligh he di e ences be ween bank up and heal hy en e p ises. This
model has been modi ied se e al imes; i s mos well-known o ms a e om 1968, 1983 and 1995.
Howe e , he use o he Al man Z-sco e o Slo ak en e p ises is mo e han ques ionable. The
unsui abili y o he model o he condi ions o Slo ak companies has been con i med by se e al
empi ical su eys. The objec i e o his s udy was o e i y he alida ion o hese h ee a ian s o
he Al man model, depending on how an unp ospe ous company is iden i ied, using a sample o
996 ag icul u al en e p ises ope a ing in he Slo ak Republic. Fou indica o s we e selec ed o he
iden i ica ion o an unp ospe ous en e p ise – economic esul s, o al liquidi y, equi y, and economic
alue added – and hey we e moni o ed o e he las yea o , as he case may be, o e he las
h ee yea s om 2014 o 2016. Using he Technique o O de o P e e ence by Simila i y o Ideal
Solu ion (TOPSIS) and Coe icien o a ia ion (CV) me hods as an objec i e me hod o weigh
de e mina ion, a combina ion o he Al man model om 1968 and he nega i e o al liquidi y in he
las e e ence yea was de e mined o be he bes . One o ou main indings is ha he way in which
an unp ospe ous en e p ise is iden i ied is a signi ican ac o a ec ing he o e all eliabili y o he
Al man model. The Al man model om 1968 and 1983 con i med he di e ences esul ing om
he na u al condi ions in which he en e p ises ope a e. The economic esul s and economic alue
added (EVA) p o ed o be inapp op ia e as indica o s o de ining an unp ospe ous en e p ise in he
condi ions o he Slo ak Republic.
Keywo ds: Unp ospe ous en e p ise, Al man model, TOPSIS echnique, Coe icien o a ia ion
me hod.
JEL Classi ica ion: B23, Q14.
APA S yle Ci a ion: Va ek, R., Gundo á, P., K a čáko á Vozá o á, I., & Ko ulič, R. (2021).
Al man Model Ve i ica ion Using a Mul i-c i e ia App oach o Slo akian Ag icul u al En e p ises.
E&M Economics and Managemen , 24(1), 146–164. h ps://doi.o g/10.15240/ ul/001/2021-1-010
In oduc ion
In he 21s cen u y, a p e equisi e o
a success ul business is good knowledge o
pas and cu en ends, o he igh long- e m
decisions o be made. Acco ding o B ealey e
al. (2011), knowing whe e a company s ands
oday is a necessa y p elude o con empla ing
whe e he company migh end up in he u u e.
One o he op ions o suppo ing sho - e m
and long- e m decisions is inancial analysis
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1, XXIV, 2021
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and inancial a ios. Financial a ios ha e
adi ionally been indica o s o a co po a e’s
o e all pe o mance (Rahman e al., 2017) and
may help o quan i y he po en ial impac o
in e nal a ings on inancial pe o mance (Belas
e al., 2012; Klieš ik e al., 2020).
The simples and na owes de ini ion o
inancial analysis is based on he ac i i ies
ha his e m includes wi hou speci ying hei
pu pose, i.e., inancial analysis is an analysis
o company da a, which is based on accoun ing
(Sů o á & Knai l, 2008). I is ocused on
e alua ing he inancial heal h o a company
and iden i ying i s weaknesses and s eng hs
(M k ička & Kolář, 2006). Acco ding o Bank
e al. (2006), his assessmen is dependen on
he company’s liquidi y and sho - e m inancial
liabili ies, which ep esen i s abili y o egula e
sou ces o unding. Acco ding o Bocha o
(2007), i is necessa y also o conside inancial
analysis in he long e m, i.e., as a sys ema ic
p ocess o con olling inancial esou ces. F om
a ime pe spec i e, we can di ide inancial
analysis in o e ospec i e ex-pos analysis
and ex-an e analysis ocusing on p edic ion.
The la e can iden i y c i ical ac o s ha could
h ea en he su i al o an en e p ise, i.e., an
app op ia e esponse o he esul s o ex-an e
analysis in he o m o eco e y measu es can
signi ican ly a ec a company’s u u e inancial
si ua ion o ensu e i s sus ainabili y. Financial
dis ess can be de ined in many di e en
ways, and simila ly, he e minology e e ing
o companies expe iencing such also di e s
– bank up , insol en , and in de aul (Čámská
& Klecka, 2020; Alaka e al., 2018). Se e al
p edic ion me hods based on ex-an e inancial
analysis ha e been e i ied o da e (e.g.
Mihalo ič, 2018; Ga ú o á e al., 2017; Ko e
al., 2017).
The aim o his s udy was o e i y he
explana o y powe o h ee a ian s o he
Al man model ( om 1968, 1983 and 1995)
depending on how a non-p ospe ous en e p ise
is iden i ied, using a sample o 996 ag icul u al
en e p ises ope a ing in Slo akia. To e i y
he ou pu s o ex-an e inancial analysis, i
is also necessa y o iden i y p ospe ous and
unp ospe ous en e p ises ( i s pa ). The e
a e usually wo app oaches, depending on
he legisla i e and heo e ical de ini ions.
The legisla i e de ini ion o an unp ospe ous
en e p ise is de e mined by he legisla ion o
a gi en coun y; in his case, we encoun e he
concep o bank up cy. The heo e ical de ini ion
is gi en by he quan i ica ion o a selec ed se
o inancial indica o s and hei subsequen
scaling (see ex an e me hods). In he ollowing
ex , he a ious app oaches aken by bo h
o eign and domes ic au ho s o de ining an
unp ospe ous en e p ise a e desc ibed, and
he equen pene a ion o indi idual c i e ia
can be obse ed. The second pa is ocused
on a se o ou own indica o s used o iden i y
an unp ospe ous en e p ise, i.e., me hodology.
The hi d pa desc ibes he esul s o ou own
esea ch, i.e., he e i ica ion o he p edic i e
abili y o he Al man model applied o a sample
o 996 ag icul u al en e p ises in he Slo ak
Republic. The use o a mul i-c i e ion app oach
in he o m o he CV-TOPSIS echnique as
a me hodological ex ension o he discussed
app oaches o he e i ica ion o he explana o y
powe o p edic ion models can be desc ibed as
o iginal and new (see Pa 1). The ou h pa
p esen s a discussion o he ob ained esul s
in he con ex o o he au ho s’ hough s and
esea ch. The las pa p esen s he conclusion
and an e alua ion o he ob ained esul s.
1. Di e en App oaches oDe ining
an Unp ospe ous En e p ise
In he p e ious sec ion, we deal wi h de ining
an unp ospe ous en e p ise om di e en
pe spec i es, i.e., hose ha can be applied
o en e p ises ega dless o he egion in
which hey a e loca ed. Fo an app op ia e
de ini ion, we conside i necessa y also o
ake in o accoun he local condi ions in which
a company ope a es. This is hen e lec ed
in a mo e p ecise de ini ion o he condi ions
unde which he en e p ise can be conside ed
unp ospe ous.
Bakeš and Valáško á (2018) p oposed
c i e ia o iden i ying an unp ospe ous
company ha would ake in o accoun cu en ly
alid Slo ak legisla ion along wi h economic
and inancial aspec s. Such c i e ia include
a a io o equi y o liabili ies o <0.08, a o al
liquidi y o <1, and nega i e ea nings a e
ax. Ďu ica (2018) desc ibed an unp ospe ous
en e p ise as an en e p ise in c isis, when he
o al amoun o hei cu en liabili ies is highe
han he alue o hei cu en asse s, he a io
o equi y o liabili ies is less han 0.04, and
he company has gene a ed a loss ( alid o
analysis in 2016). Klieš ik e al. (2018) and
Mendelo á and Bieliko á (2017) iden i ied an
148 2021, XXIV, 1
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unp ospe ous en e p ise as one ha mee s he
c i e ion ound in applicable legisla ion o he
Slo ak Republic, i.e., he alue o i s liabili ies
due exceeds he alue o i s asse s, o he
en e p ise is in nega i e equi y.
Bieliko á e al. (2014) desc ibed a mo e
complex iew, exp essed by h ee c i e ia
acco ding o which an en e p ise can be
conside ed unp ospe ous, namely, i i :
 Mee s he legisla i e de ini ion o an
en e p ise in he Slo ak Republic, i.e., he
en e p ise is obliged o conduc accoun ing
p ocedu es acco ding o a special
egula ion, i has mo e han one c edi o
and he alue o i s liabili ies exceeds he
alue o i s asse s, i.e., he en e p ise is in
nega i e equi y;
 Has made a loss o wo consecu i e yea s;
 Has a nega i e e u n on sales (ROS) and
o al liquidi y (L3) less han 1.
This se o c i e ia was also used by
Bieliko á (2016), who addi ionally ake in o
accoun he ollowing:
 The legisla i e de ini ion o a company in
p olonga ion in he Slo ak Republic, i.e.,
he same c i e ion as in he p e ious case;
 The Eu opean Union guidelines 2004/C
244/02 on s a e aid o escuing and
es uc u ing i ms in di icul y, which de ine
a i m in di icul y as one in which mo e han
hal o he basic capi al is co e ed by loss
and mo e han a qua e o ha basic capi al
was co e ed by loss du ing he p e ious 12
mon hs;
 A loss in wo consecu i e pe iods.
Boďa and Ú adníček (2016) and K áľ e
al. (2016) p esen ed a se o h ee c i e ia o
iden i ying an unsuccess ul business. These
c i e ia include nega i e equi y and ea nings
a e ax (EAT <0), as well as a o al liquidi y
(L3) less han 1. Acco ding o Valáško á e al.
(2018a, 2018b), an unp ospe ous company
is one wi h a a io o equi y o o al deb less
han 0.4, a o al liquidi y (L3) less han 1, and
nega i e ea nings a e ax (EAT). Acco ding o
Ko áčo á and Kubala (2018), i is an en e p ise
ha :
 Did no achie e posi i e equi y, o in o he
wo ds, he di e ence be ween asse s and
liabili ies, including he acc ual o liabili ies,
was nega i e;
 Had a leas wo mone a y liabili ies mo e
han 30 days o e due (because we we e
unable o iden i y his in o ma ion di ec ly
om he inancial s a emen s, i has been
eplaced by a de e mina ion o he o e all
liquidi y indica o h eshold, i.e., L3 <1);
 Exhibi ed he ollowing alues o he sel -
inancing coe icien (equi y and liabili ies
a io): in 2016, <0.08; in 2015, <0.06; and
in 2014, <0.04.
Fo an independen g oup o au ho s, he
key c i e ion o assessing business p ospe i y
is he economic alue added, which ep esen s
an agg ega e cha ac e is ic o a company’s
inancial pe o mance. This g oup includes
Šo anko á e al. (2017), Neumaie o á and
Neumaie (2016), Čámská (2016), Maňaso á
(2008) and o he s; in all cases, an unp ospe ous
en e p ise is one ha has achie ed nega i e
economic alue added in a ce ain pe iod.
Along wi h Lesáko á e al. (2015), Zalai e
al. (2013) and o he s, we conside economic
alue added as an impo an c i e ion, as he e
has been a ecen shi in hinking away om
adi ional indica o s owa ds he ma ke alue
o a company. This is con i med by he ac ha
he EVA indica o is now inc easingly being
used in inancial managemen and decision-
making.
2. TheAl manModelasaMe hod
o Mul idimensionalDisc imina ion
Analysis
As a esul o he ecen wo ldwide inancial
c isis and economic ecession, he demand o
bank up cy-p edic ion models and inancial-
isk analysis has gained s ong a en ion. The
inabili y o accu a ely p edic bo h bank up cy
and c edi isk can ha e de as a ing socio-
economic e ec s (An unes e al., 2017). To
da e, many models o p edic bank up cy ha e
been in oduced, bu esea ch in his ield
is e e cons an (Le e al., 2018; Zelenko
e al., 2017). Se e al au ho s (Alaka e al.,
2018; Ka as & Režnáko á, 2012; Sušický,
2011) a gue ha me hods o mul idimensional
disc imina ion analysis a e he wo ld’s mos
widely used me hods o p edic ing he inancial
heal h o businesses. Among hei suppo e s
a e Balcaen and Oooghe (2006) and Sun e al.
(2014), who app ecia e hei good classi ica ion
capabili y.
The ounde and pionee o he use o
mul idimensional disc imina ion analysis is
Al man (1968). The Al man Z-sco e is cu en ly
he mos well-known and widely used p edic ion
model (Ga ú o á e al., 2017; Delina & Packo á,
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2013). I is o en modi ied and e i ied o he
needs o na ional economics. In he Slo ak
Republic, hese applica ions a e o e ed by
Kabá (2011a) and Boďa and Ú adníček (2016,
2019); in he Czech Republic, by Schön eld e
al. (2018) and Režňáko á and Ka as (2015);
and ab oad, by Li and Fa (2019), Almany e al.
(2016), Sulub (2014) and Li schu z and Jacobi
(2010).
The model was c ea ed using a sample o
33 US companies ha wen bank up be ween
1946 and 1965, while a second g oup included
33 US companies ha p ospe ed in his pe iod
(Kočišo á & Mišanko á, 2014). Al man (2002)
conside ed he limi ed da a a ailable o be
a majo p oblem, causing he g oup o selec ed
businesses o be ela i ely he e ogeneous.
The au ho ini ially wo ked wi h a se o 22
selec ed inancial indica o s om i e classes –
liquidi y, p o i abili y, deb , sol ency and ac i i y
(Hosaka, 2019; Kabá , 2011a). Conce ning
Al man’s Z-sco e, i ms a e g ouped in o he
h ee zones o disc imina ion iden i ied by
Al man: he Dis ess Zone, G ey Zone and Sa e
Zone (Meggison e al., 2019). Al man’s goal
was o selec a small numbe o a io indica o s
ha would bes highligh he di e ence be ween
a bank up and a heal hy en e p ise. Ra io
indica o s we e selec ed based on he g ea es
di e ences in he alues be ween he di e en
se s o en e p ises (see Tab. 1).
In his manne , Al man c ea ed a i e-
ac o model. In he o iginal s udy om 1968,
he success ully classi ied 94% o bank up
US en e p ises and 97% o p ospe ous US
p oduc ion en e p ises based on a Z-sco e
wi h an annual ad ance. In he 30 yea s
ollowing he c ea ion o he model, he es ed
i s p edic i e abili y, and ano he 86 p oblema ic
en e p ises we e analyzed om 1969 o
1975. F om 1976 o 1995, Al man es ed 110
bank up en e p ises, and in he pe iod om
1997 o 1999, he numbe o en e p ises
wen up o 120. The h eshold o p oblema ic
businesses was se a 2.67, and businesses
we e only es ed wo yea s be o e bank up cy
(Maňaso á, 2008). Al man (2006) s a es ha
he main eason o he highe e o a e o he
model is ha , a ha ime, US businesses we e
a highe isk compa ed o when he model was
c ea ed. The highe isk le el is e lec ed in he
change in he a iables X2 and X4. In 1983, an
upda ed Al man Z-sco e model was c ea ed ( o
businesses ha did no ha e publicly aded
sha es) and included he same a io indica o s
as he o iginal model. Howe e , he weigh s o
he indi idual a io indica o s we e changed,
and hus, he e alua ion c i e ia also changed.
The same changes ook place in 1995, when
a hi d model was c ea ed o he pu pose o
e alua ing non-p oduc i e en e p ises; i was
also used in i s own esea ch. E en Al man’s
models based on mul iple disc iminan analysis
ha e p o ed qui e success ul and s ood up
o c i icism (Pe ei a e al., 2016). Acco ding
o Klieš ik e al. (2015), he limi a ions o he
models a e as ollows. The models ake only
a no mal dis ibu ion o independen a iables
in o accoun , conside only homogenei y o he
a ia ion-co a ia ion ma ix, and assume only
a linea ela ionship be ween he independen
a iables. Al man’s models a e accoun ing-
based, which educes hei abili y o p edic
inancial dis ess and bank up cy eliably. Li
and Fa (2019) a gue ha unde he going-
conce n p inciple, hei applica ion is limi ed, as
p edic ions o a i m’s u u e inancial condi ion
may be less in o ma i e when hey a e based
on he i m’s pas pe o mance.
Indica o Heal hy en e p ises Bank up en e p ises
Wo king capi al/ o al asse s X10.414 −0.061
Re ained ea nings/ o al asse s X20.355 −0.626
Ea nings be o e in e es and ax/ o al asse s X30.154 −0.318
Ma ke capi alisa ion/ o al liabili ies X42.477 0.401
Sales/ o al asse s X51.900 1.500
Sou ce: Al man (1968)
Tab. 1: A e age alues o Al man es indica o s in 1968
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3. Resea chMe hodology
A e a heo e ical o e iew o he di e en iews
on wha cons i u es an unp ospe ous en e p ise
and a speci ica ion o he basics o he Al man
model, i is possible o de ine he aim o he
p esen ed manusc ip as a e i ica ion o he
Al man model’s p edic i e abili y depending on
how an unp ospe ous en e p ise is iden i ied.
Based on he heo e ical de ini ion o he
di e en iews on wha highligh s an unp ospe ous
en e p ise, we p esen a summa y o e iew
(Tab. 2), which also se es o de ine i s own iew.
Fo he pu poses o he u he analysis
o unp ospe ous en e p ises, we will conside
ones ha mee :
 Sepa a ely, one o he ou condi ions
e e ed o abo e in he las e e ence yea ,
2016 (Va ian s A1, A2, A3, A4);
 Sepa a ely, one o he ou condi ions
e e ed o abo e h oughou he pe iod
unde e iew, in 2014, 2015 and 2016
(Va ian s B1, B2, B3, B4);
 A he same ime, all ou o he abo e
condi ions in he las e e ence yea , 2016
(Va ian C).
Wi hin he amewo k o he p esen ed
esea ch, we discuss he explana o y abili y
o h ee a ian s o he Al man model, i.e., he
models om 1968, 1983 and 1995 ( o mo e
de ails and di e ences, see Ko ulič e al., 2018),
which a e calcula ed as ollows:
Z1968 = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 0.999X5 (1)
Z1968 = 0.717X1 + 0.847X2 + 3.107X3 +
+ 0.420X4 + 0.998X5 (2)
Z1995 = 6.56X1 + 3.26X2 + 6.72X3 + 1.05X4 (3)
whe e: X1 = Ne wo king capi al/ o al asse s;
X2 = Re ained ea nings/ o al asse s;
X3 = Ea nings be o e in e es and ax/
o al asse s;
X4 = Ma ke alue o equi y/ o al
liabili ies;
X5 = Sales/ o al asse s.
As can be seen om he cons uc ion o
indi idual models o modi ica ions o he Al man
model, he s uc u e o he indica o s used
emains he same. Views on hei impo ance
has changed o e he yea s, exp essed by
a change in he weigh s assigned o each
indica o . These changes in weigh we e
subsequen ly e lec ed in a change in he
in e als/bounda ies o he iden i ica ion o an
unp ospe ous en e p ise, o a heal hy one, as
he case may be (Tab. 3).
The explana o y abili y o he Al man model
is subsequen ly e i ied by he calcula ion o
he ype I e o (α), ype II e o (β) and o e all
eliabili y, which a e shown in Tab. 4.
Acco ding o Ga ú o á e al. (2017) and
Delina and Packo á (2013), he ollowing
calcula ion is based on he abo e able o :
 Type I e o , i.e., he p opo ion o
misclassi ied bank up companies ( he
alse-nega i e a e):
FNR = FN
TP + FN (4)
Va ian Condi ion Au ho
A1 B1
C
1. P o i < 0
Bakeš & Valáško á, 2018; Ďu ica, 2018; Valáško á e al.,
2018a, 2018b; Boďa & Ú adníček, 2016; K áľ e al., 2016;
Bieliko á e al., 2014
A2 B2 2. Equi y < 0
Klieš ik e al., 2018; Ko áčo á & Kubala, 2018;
Mendelo á & Bieliko á, 2017; Boďa & Ú adníček, 2016;
K áľ e al., 2016; Bieliko á e al., 2014
A3 B3 3. L3 < 1
Bakeš & Valáško á, 2018; Ko áčo á & Kubala, 2018;
Valáško á e al., 2018a, 2018b; Boďa & Ú adníček, 2016;
K áľ e al., 2016; Bieliko á e al., 2014
A4 B4 4. EVA < 0,
(EAT − e × E) < 0
Šo ánko á e al., 2017; Čámská, 2016; Neumaie o á &
Neumaie , 2013, 2016; Maňaso á, 2008
Sou ce: own
Tab. 2: Condi ions o iden i ying an unp ospe ous en e p ise

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 Type II e o , i.e., he p opo ion o
misclassi ied p ospe ous companies ( he
alse-posi i e a e):
FPR = FP
FP + TN (5)
 O e all eliabili y (o e all accu acy), i.e., he
p opo ion o co ec ly classi ied en e p ises:
ACC = TP + TN
TP + TN + FP + FN (6)
The da a o he analyses we e d awn om
da a o ag icul u al companies (balance shee s
and p o i and loss s a emen s) p o ided by he
Minis y o Ag icul u e o he Slo ak Republic in
he o m o in o ma ion shee s o anonymous
ag icul u al subjec s. The o al ile included 1,867
subjec s o legal and na u al pe sons wi h up o
19 and 20 o mo e employees in he pe iod 2014–
2016. By using he SOFINA_s anda d economic
so wa e o inancial planning and manage ial
economy, we iden i ied 996 businesses ( om
he o al se ) o which he e was a con inuous
eco d o inancial da a o he e e ence pe iod
and which had ull eco ds o balance shee s and
inancial s a emen s (see Fig. 1).
Di e ences in he economic esul s o hese
en i ies can also be obse ed wi h espec o
he na u al condi ions in which hey ope a e.
Ko ulič e al. (2017) di ided he e i o y o he
Slo ak Republic in o wo g oups (Fig. 2) on his
basis.
Financial p oblems G ay zone Heal hy en e p ise
Z-sco e (1968) – A68 <1.81 <1.81–2.99> >2.99
Z-sco e (1983) – A83 <1.2 <1.2–2.9> >2.9
Z-sco e (1995) – A95 <1.1 <1.1–2.6> >2.6
Sou ce: Boďa and Ú adníček (2016)
P edic ion-bank up cy P edic ion-non-bank up cy
Fac -bank up cy he co ec esul (TP) e o ype I (FN)
Fac -non-bank up cy e o ype II (FP) he co ec esul (TN)
Sou ce: Klepáč and Hampel (2017)
Tab. 3: E alua ion bounda ies o indi idual Al man models
Tab. 4: Type I and II e o
Fig. 1: S uc u e o he esea ch sample
Sou ce: own
152 2021, XXIV, 1
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The me hod o Damoda an (2004, 2014)
was used o calcula e he cos o equi y capi al
( e) acco ding o he EVA indica o (Tab. 2); i
was also applied by Šo ánko á e al. (2017)
and Mařík e al. (2011). The analyses we e
pe o med in MS Excel, S a is ica 13.4 and
S a g aphics XVIII.
3.1 TOPSISTechniqueasaTool o 
Assessing heExplana o yAbili y
o  heModel
MCDM (Mul i C i e ia Decision Making)
me hods we e de eloped o assis decision-
making ega ding ei he anking a known
se o al e na i es o a p oblem o making
a choice om among his se while conside ing
he con lic ing c i e ia (Ma dani e al., 2016).
Acco ding o Za adskas e al. (2014), he
Technique o O de o P e e ence by Simila i y
o Ideal Solu ion (TOPSIS) is one o he mos
widely used MCDM me hods. The o igin o his
me hod can be a ibu ed o Hwang and Yoon
(1981) and Yoon (1980), who de eloped i as
an al e na i e o he ELECTRE me hod. The
esul o he TOPSIS echnique is desc ibed
by S eimikine e al. (2012) as a solu ion
wi h he sho es dis ance o a posi i e-ideal
solu ion (PIS), in e ms o Euclidean dis ance.
The TOPSIS me hod o e s a solu ion ha is
he closes o he abo emen ioned PIS unde
he gi en condi ions and, a he same ime,
he a hes om he nega i e-ideal solu ion
(NIS) (Za adskas e al., 2016). The TOPSIS
echnique was pe o med acco ding o Va ek
and Bečica (2020) and Va ek (2019).
The indica o s used o he abo e
calcula ion a e he esul o an e alua ion o he
Al man model’s explana o y abili y:
 I1 = Type I e o (FNR) wi h a minimizing
cha ac e ;
 I2 = Type II e o (FPR) wi h a minimizing
cha ac e ;
 I3 = O e all eliabili y (ACC) wi h
a maximizing cha ac e .
Fo each o he MCDM me hods, he i s
and essen ial s ep is de e mining he weigh s
o he indi idual indica o s. Ke šuliene e al.
(2010) di ide he app oaches o weigh ing
in o ou g oups: subjec i e, expe , objec i e
and in eg a ed (which combines he p e ious
app oaches). Subjec i e me hods e lec he
decision-make ’s pe sonali y and indi idual
p e e ences. Objec i e me hods de e mine
weigh s based on a p ede e mined ma hema ical
model unique o each me hod, wi h he decision-
make ha ing no in luence on he ou come. They
include CRITIC (CRi e ia Impo ance Th ough
Fig. 2: Spa ial dis ibu ion o analyzed subjec s (LFA – he dis ic s wi h wo se na u al
condi ions; NONLFA – he dis ic s wi h be e na u al condi ions)
Sou ce: own
153
1, XXIV, 2021
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In e c i e ia Co ela ion), MW (mean weigh ), SD
(s anda d de ia ion), SVP (S a is ical Va iance
P ocedu e) and o he s (see Sude & Kah aman,
2018; Yalcin & Unlu, 2018, and o he s). Fo ou
own p ocessing, he Coe icien o a ia ion
me hod (CV) was used, which was de ised by
Singla e al. (2017) and u he desc ibed in he
s udies o Va ek and Cho anco á (2019) and
Yalcin and Unlu (2018).
The aim o he CV-TOPSIS combina ion is
an objec i e assessmen o he Al man model’s
explana o y abili y o indi idual a ian s, which
would e lec he eliabili y o no only he model
(ACC) as a whole bu also speci ic esul s (FNR
and FPR), which we belie e should also be
conside ed. These esul s a e supplemen ed by
addi ional ma hema ical and s a is ical me hods
o which we can add he Mann-Whi ney es
(W), K uskal-Wallis es (Q), Le ene es (LE)
and Kolmogo o -Smi no es (K-S).
4. Resea chResul s
The esul s o ou own esea ch can be di ided
in o se e al sepa a e pa s. In he i s , he o e all
e alua ion esul s a e desc ibed and s a is ically
compa ed. In he second, he e alua ion o a se
o 996 en i ies is ca ied ou sepa a ely using
each condi ion o iden i ying unp ospe ous
en e p ises in he las moni o ed yea , 2016 (i.e.,
Va ian s A1, A2, A3, A4), one o he condi ions
o he las h ee yea s is ul illed sepa a ely (i.e.,
Va ian s B1, B2, B3, B4), and all ou condi ions
o iden i ying unp ospe ous en e p ises in he
las yea o he pe iod unde e iew a e hen
ul illed simul aneously (i.e., Va ian C). The las
pa is a mul i-c i e ia e alua ion o he ob ained
esul s using he CV-TOPSIS echnique.
4.1 O e allE alua ionResul s
wi h heAl manModel
The a iabili y o he o e all e alua ion o
he esul s using he a ian s o he Al man
model ( om he yea s 1968, 1983 and 1995)
is shown in Fig. 3, om which di e ences can
be iden i ied, especially when compa ing he
ange o a ia ion (RA68 = 71.31, RA83 = 50.39,
and RA95 = 162.40), which, in combina ion wi h
he changing subjec -classi ica ion in e als,
unde lines o e all signi ican di e ences
(Q = 26.667; p < 0.01; LE = 121.036; p < 0.01).
Howe e , he pa icula a ian o he Al man
model does no a ec he shape o he o e all
esul s o hei dis ibu ion unc ion, because in
all h ee cases, we can conside he esul s o
be posi i ely skewed and mo e poin ed han
a no mal dis ibu ion.
Fig. 3: O e all esul s o he e alua ion o subjec s wi h he Al man model (Z-sco e)
Sou ce: own
154 2021, XXIV, 1
Finance
This s uc u e o he absolu e esul s is
e lec ed in a classi ica ion o he inancial
heal h o indi idual en e p ises (Fig. 4). The
Al man model om 1968 and 1983 ma ked
he inancial heal h o he majo i y o he a ed
en i ies as nega i e, and signaled inancial
p oblems o hese en i ies in he upcoming
pe iod (60% o 53%, as he case may be). By
con as , he Al man model om 1995 indica ed
a sa is ac o y inancial si ua ion o up o 43% o
all he en i ies (426).
Di e ences in inancial heal h can also
be obse ed when compa ing en e p ises
ope a ing in be e , o wo se, na u al condi ions
(LFA/NONLFA). S a is ically signi ican
di e ences we e ound in he case o he Al man
model om 1968 and 1983, when no only he
median alue bu also he o e all s uc u e o
he esul s, i.e., hei dis ibu ion unc ion, was
di e en (see Tab. 5).
The assessmen o inancial heal h h ough
a ian s o he Al man model om 1968 and
1983 is de e mined by he quali y o he soil, i.e.,
he na u al condi ions. S a is ically signi ican
di e ences using hese a ian s we e also
demons a ed in he dis ibu ion unc ions,
bu we no e hei homoskedas ici y. Howe e ,
in he case o he 1995 model, he na u al
condi ions did no in luence his assessmen .
Pa adoxically, subjec s ope a ing in dis ic s wi h
be e na u al condi ions (NONLFA) showed
a be e a e age a ing. Based on hese esul s,
we can say ha e en in he 21s cen u y, he
assessmen o inancial heal h using he Al man
Fig. 4: Classi ica ion o he inancial heal h o subjec s acco ding o he Al man model
Sou ce: own
Model Medians check Va iance check DF check A e age
LFA NON
Al man 68 W = 131417 (<0.01) LE = 0.007 (0.934) K-S = 1.996 (<0.01) 2.37 1.99
Al man 83 W = 136857 (<0.01) LE = 0.0003 (0.985) K-S = 2.483 (<0.01) 1.90 1.51
Al man 95 W = 120612 (0.287) LE = 0.039 (0.843) K-S = 0.910 (0.383) 3.18 3.08
Sou ce: own
Tab. 5: Compa ison o esul s o he Al man model (LFA/NONLFA)
161
1, XXIV, 2021
Finance
his egion. In addi ion, we plan, in he u u e, o
e i y he p edic i e abili ies o he Gu čík index
and Ch as ino a model, which we e designed
exp essly o he needs o Slo ak a ms.
Ano he limi a ion is he e i o y o he Slo ak
Republic. In o de o inc ease he objec i i y o
he esea ch esul s, we ecommend ex ending
he esea ch sample o subjec s wo king he
soil in o he V4 coun ies and compa ing hem.
Acknowledgmen s: Suppo ed by he g an
No. CZ.02.2.69/0.0/0.0/16_027/0008493 “In e -
na ional mobili y o TUL esea che s” o he
“Minis y o Educa ion, You h and Spo o he
Czech Republic”, he g an No. 024PU-4/2020
“Inno a ion o he s uc u e, con en and way
o eaching economic subjec s o he s udy
p og am Managemen and En i onmen al
Managemen a he PhD le el” o he “Cul u al
and Educa ional G an Agency o he Minis y
o Educa ion, Science, Resea ch and Spo o
he Slo ak Republic”, he g an No. 1/0578/18
“Modi ica ion o me hodologies o sus ainable
assessmen and managemen ” o he “Scien i ic
G an Agency o he Minis y o Educa ion,
Science, Resea ch and Spo o he Slo ak
Republic and he Slo ak Academy o Sciences”.
Re e ences
Alaka, H. A., Oyedele, L. M., Owolabi, H. A.,
Kuma , V., Ajayi, S. O., Akinade, O. O., & Bilal,
M. (2018). Sys ema ic e iew o bank up cy
p edic ion models: Towa ds a amewo k o
ool selec ion. Expe Sys ems wi h Applica ion,
94, 164–184. h ps://doi.o g/10.1016/j.
eswa.2017.10.040
Almamy, J., As on, J., & Ngwa, L. N. (2016).
An e alua ion o Al man’s Z-sco e using cash
low a io o p edic co po a e ailu e amid he
ecen inancial c isis: E idence om he UK.
Jou nal o Co po a e Finance, 36, 278–285.
h ps://doi.o g/10.1016/j.jco p in.2015.12.009
Al man, E. I. (2002). Bank up cy, c edi isk,
and high yield junk bonds. Malden: Blackwell.
Al man, E. I., & Ho chkiss, E. (2006).
Co po a e Financial Dis ess and Bank up cy:
P edic and A oid Bank up cy, Analyze and
In es in Dis essed Deb . New Yo k, NY: Wiley.
h p://doi.o g/10.1002/9781118267806
Al man, E. I. (1968). Financial Ra ios,
Disc iminan Analysis and he P edic ion
o Co po a e Bank up cy. The Jou nal
o Finance, 23(4), 589–609. h ps://doi.
o g/10.1111/j.1540-6261.1968. b00843.x
Al man, E. I., Iwanicz-D ozdowska, M.,
Lai inen, E. K., & Su as, A. (2017). Financial
Dis ess P edic ion in an In e na ional Con ex :
A Re iew and Empi ical Analysis o Al man’s
Z-sco e Model. Jou nal o In e na ional
Financial Managemen & Accoun ing, 28(2),
131–171. h ps://doi.o g/10.1111/ji m.12053
An unes, F., Ribei o, B., & Pe ei a, F. (2017).
P obabilis ic modelling and isualiza ion o
bank up cy p edic ion. Applied So Compu ing,
60, 831–843, h ps://doi.o g/10.1016/j.
asoc.2017.06.043
Bakeš, V., & Valáško á, K. (2018). Applica-
ion and e i ica ion o Slo ak p edic ion models
in condi ions o na ional economy. Podniko á
ekonomika a manažmen . Elek onický časopis
o ekonomike, manažmen e, ma ke ingu
a logis ike podniku, 2, 3–15.
Balcaen, S., & Ooghe, H. (2006). 35 yea s o
s udies on business ailu e: An o e iew o he
classic s a is ical me hodologies and hei ela ed
p oblems. The B i ish Accoun ing Re iew, 38(1),
63–93. h p://doi.o g/10.1016/j.ba .2005.09.001
Bank, V., Ta asquina, A., & Bank, S. (2006).
Financial analysis. Moscow: P ospec .
Belas, J., Cipo o a, E., No ak, P., & Polach,
J. (2012). Impac s o he Founda ion In e nal
Ra ings Based App oach Usage on Financial
Pe o mance o Comme cial Bank. E&M
Economics and Managemen , 15(3), 142–154.
Bieliko á, T. (2016). Ino a í ne možnos i
diagnos iko ania inančného zd a ia ý obného
podniku o äzbe na jeho inančno-ekonomickú
ýkonnosť. Banská Bys ica: EF UMB.
Bieliko á, T., Cú , S., & Ú adníček, V. (2014).
The in luence o he de ini ion o isky company
on inancial si ua ion diagnos ic models in
Slo ak dynamic economic en i onmen . In M.
Čulík (Ed.), Managing and modelling o inancial
isks: P oceedings om 7 h in e na ional
scien i ic con e ence (pp. 38–45). Os a a: VSB
– Technical Uni e si y o Os a a.
Bocha o , V. (2007). Financial analysis.
Sain Pe e sbu g: Pe e P ess.
Boďa, M., & Ú adníček, V. (2016). The
po abili y o Al man’s Z-sco e model o
p edic ing co po a e inancial dis ess o Slo ak
companies. Technological and Economic
De elopmen o Economy, 22(4), 532–553.
h ps://doi.o g/10.3846/20294913.2016.1197165
Boďa, M., & Ú adníček, V. (2019).
P edic ing Financial Dis ess o Slo ak
Ag icul u al En e p ises. Ekonomický časopis,
67(4), 426–452.

162 2021, XXIV, 1
Finance
B ealey, R. A., Mye s, S. C., & Allen, F.
(2011). P inciples o Co po a e Finance. New
Yo k, NY: McG aw-Hill/I win.
Čámská, D. (2016). Accu acy o Models
P edic ing Co po a e Bank up cy in a Selec ed
Indus y B anch. Ekonomický časopis, 64(4),
353–366.
Čámská, D., & Klecka, J. (2020).
Compa ison o P edic ion Models Applied in
Economic Recession and Expansion. Jou nal
o Risk and Financial Managemen , 13(3),
1–16, h ps://doi.o g/10.3390/j m13030052
Damoda an, A. (2004). Valua ion he Big
Pic u e. Re ie ed Oc obe 10, 2019, om
h p://people.s e n.nyu.edu/adamoda /pd iles/
coun y/B azilJune04.pd
Damoda an, A. (2014). Equi y Risk
P emiums: Looking Backwa ds and Fo wa ds.
Re ie ed Oc obe 15, 2019, om h p://people.
s e n.nyu.edu/adamoda /pd iles/coun y/ERP.pd
Delina, R., & Packo á, M. (2013). P edic ion
bank up cy models alida ion in Slo ak
business en i onmen . E&M Economics and
Managemen , 16(3), 101–110.
Ďu ica, M. (2018). Decision T ee Financial
Dis ess P edic ion Model o Slo ak Companies.
Podniko á ekonomika a manažmen , 2, 16–26.
Ga ú o á, B., Packo á, M., Mišanko á, M.,
& Sm čka, Ľ. (2017). P edic i e po en ial and
isks o selec ed bank up cy p edic ion models
in he Slo ak business en i onmen . Jou nal o
Business Economics and Managemen , 18(6),
1156–1173. h ps://doi.o g/10.3846/16111699.2
017.1400461
Hosaka, T. (2019). Bank up cy p edic ion
using imaged inancial a ios and con olu ional
neu al ne wo ks. Expe Sys ems wi h Applica ion,
117, 287–299.
Hwang, C.-L., & Yoon, K. (1981). Mul iple
A ibu e Decision Making Me hods and
Applica ions: A S a e-o - he-A Su ey. Be lin,
Heidelbe g: Sp inge -Ve lag.
Kabá , L. (2011a). Ako ďalej aplikácii
Al mano ho modelu? Finančný manažé , 11(1),
7–9.
Kabá , L. (2011b). P oblémy aplikácie boni ných
a p edikčných modelo podnika eľskom
p os edí SR. Finančný manažé , 11(3), 89–90.
Ka as, M., & Řežnáko á, M. (2012). Financial
Ra ios as Bank up cy P edic o s: The Czech
Republic Case. In D. Pa elko á, J. S ouhal, & M.
Paseko a (Eds.), P oceeding o he 1s WSEAS
In e na ional Con e ence on Finance, Accoun ing
and Audi ing (pp. 56–67). A hen: WSEAS.
Ke šuliene, V., Za adskas, E. K., & Tu skis,
Z. (2010). Selec ion o a ional dispu e esolu ion
me hod by applying new s ep-wise weigh
assessmen a io analysis (SWARA). Jou nal
o Business Economics and Managemen ,
11(2), 1611–1699. h ps://doi.o g/10.3846/
jbem.2010.12
Klepáč, V., & Hampel, D. (2017). P edic ing
inancial dis ess o ag icul u e companies in
EU. Ag icul u al Economics, 63(8), 347–355.
h ps://doi.o g/10.17221/374/2015-AGRICECON
Klieš ik, T., Kočišo á, K., & Mišanko á,
M. (2015). Logi and P obi Model used o
P edic ion o Financial Heal h o Company.
P ocedia Economics and Finance, 23, 850–855.
Klieš ik, T., Mišanko á, M., Valaško á, K.,
& S abo á, L. (2018). Bank up cy P e en ion:
New E o o Re lec on Legal and Social
Changes. Science and Enginee ing E hics,
24(2), 791–803. h p://doi.o g/10.1007/s11948-
017-9912-4
Klies ik, T., Valasko a, K., Laza oiu, G.,
Ko aco a, M., & V bka, J. (2020). Remaining
Financially Heal hy and Compe i i e: The
Role o Financial P edic o . Jou nal o
Compe i i eness, 12(1), 74–92, h ps://doi.
o g/10.7441/joc.2020.01.05
Ko, Y. C., Fuji a, H., & Li, T. (2017). An
e iden ial analysis o Al man Z-sco e o
inancial p edic ions: case s udy on sola ene gy
companies. Applied So Compu ing, 52, 748–
759. h ps://doi.o g/10.1016/j.asoc.2016.09.050
Kočišo á, K., & Mišanko á, M. (2014).
Disc iminan Analysis as a Tool o Fo ecas ing
Company’s Financial Heal h. P ocesia – Social
and Beha io al Sciences, 110, 1148–1157.
h ps://doi.o g/10.1016/j.sbsp o.2013.12.961
Ko ulič, R., Adamišin, P., K a čáko á
Vozá o á, I., & Va ek, R. (2017). The impac
o managemen skills o ag icul u al en i ies in
ela ion o economic e iciency and Na u al-
Clima ic condi ions in Slo akia. Jou nal o
En i onmen al Managemen and Tou ism, 8(1),
92–99. h ps://doi.o g/10.14505//jem . 8.1(17).09
Ko ulič, R., Ki ály, P., & Rajčánio á, M.
(2018). Finančná analýza podniku. B a isla a:
Wol e s Kluwe SR.
Ko áčo á, M., & Kubala, P. (2018).
Ve i ica ion o P edic ion Models Based on
Disc iminan Analysis in Condi ions o Slo ak
Republic. Podniko á ekonomika a manažmen ,
2, 52–64.
K áľ, P., Fleische , M., S acho á, M., &
Nedelo á, G. (2016). Co po a e inancial
163
1, XXIV, 2021
Finance
dis ess p edic ion o Slo ak companies:
Z-sco e models s. al e na i es. In M. Boďa,
V. Mendelo á (Eds.), AMSE 2016 – 19 h
Applica ions o Ma hema ics and S a is ics in
Economics Con e ence P oceedings (pp. 224–
231). Banská Š ia nica: UMB.
Le, T., Lee, M. Y., Pa k, J. R., & Baik, S.
W. (2018). O e sampling echniques o
bank up cy p edic ion: No el ea u es om
a ansac ion da ase . Symme y-Basel, 10(4),
1–13. h ps://doi.o g/10.3390/sym10040079
Lesáko á, Ľ., Elexa, Ľ., & Gundo á,
P. (2015). Finančno-ekonomická analýza
podniku 2. Banská Bys ica: UMB.
Li, L., & Fa , R. (2019). P edic ing co po a e
bank up cy: Wha ma e s? In e na ional
Re iew o Economics and Finance, 62, 1–19.
Li schu z, S., & Jacobi, A. (2010). P edic ing
bank up cy: e idence om Is ael. In e na ional
Jou nal o Business and Managemen , 5(4),
133–141. h ps://doi.o g/10.5539/ijbm. 5n4p133
Maňaso á, Z. (2008). Úpadky podniků
České epublice a možnos i jejich časné
p edikce. P ague: P ague Uni e si y o
Economics and Business.
Ma dani, A., Za adskas, E. K., Go indan,
K., Senin, A. A., & Jusoh, A. (2016). VIKOR
Technique: A Sys ema ic Re iew o he
S a e o he A Li e a u e on Me hodologies
and Applica ions. Sus ainabili y, 8(1), 1–38.
h ps://doi.o g/10.3390/su8010037
Mařík, M., Čada, K., Dušek, D., Maříko á,
P., Rýdlo á, B., & Rajdl, J. (2011). Me ody
oceňo ání podniku: p oces ocenění – základní
me ody a pos upy. P ague: Ekop ess.
Megginson, W. L., Meles, A., Sampagna o,
G., & Ve doli a, V. (2019). Financial Dis ess
Risk in Ini ial Public O e ings: How Much
Do Ven u e Capi alis s Ma e ? Jou nal o
Co po a e Finance, 59, 10–30. h ps://doi.
o g/10.1016/j.jco p in.2016.09.007
Mendelo á, V., & Bieliko á, T. (2017).
Diagnos iko anie inančného zd a ia podniko
pomocou me ódy DEA: Aplikácia na podniky
Slo enskej Republike. Poli ická ekonomie,
65(1), 26–44. h ps://www.doi.o g/10.18267/j.
polek.1125
Mihalo ič, M. (2018). Využi ie skó ingo ých
modelo při p edikcii úpadku ekonomických
subjek o Slo enskej epublike. Poli ická
ekonomie, 66(6), 689–708. h ps://doi.
o g/10.18267/j.polek.1226
M k ička, J., & Kolář, P. (2006). Financial
analysis. P ague: ASPI.
Neumaie o á, I., & Neumaie , I. (2013).
Vypo ídací schopnos Indexu IN05. In
Ekonomika pohybu: Sbo ník příspě ků
z meziná odní kon e ence pořádané
u příleži os i šedesá ého ý očí VŠE a akul y
[Economy in mo ion: P oceedings om he
in e na ional con e ence o ganized on he
occasion o he 60 h anni e sa y o Uni e si y
o Economics and he acul y] (pp. 169–176).
P ague: P ague Uni e si y o Economics and
Business.
Neumaie o á, I., & Neumaie , I. (2016). The
Pe o mance Ranking o Chosen Manu ac u ing
Di ision. In J. K ajíček, J. Nešleha, & K.
U bano ský (Eds.), 13 h In e na ional Scien i ic
Con e ence o he Eu opean Financial Sys ems
(pp. 502–507). B no: Masa yk Uni e si y.
Pe ei a, J., Bas o, M., & da Sil a, A. (2016).
The Logis ic Lasso and Ridge Reg ession
in P edic ing Co po a e Failu e. P ocedia
Economics and Finance, 39, 634–641.
Pi o á, K. (2011). Possibili ies o he Al man
Ze a Model Applica ion o Czech Fi ms. E&M
Economics and Managemen , 14(3), 66–76.
Rahman, A., Belas, J., Klies ik, T., & Tyll,
L. (2017). Colla e al equi emen s o SME
loans: empi ical e idence om he Viseg ad
coun ies. Jou nal o Business Economics and
Managemen , 18(4), 650–675. h ps://www.doi.
o g/10.3846/16111699.2017.1357050
Režnáko á, M., & Ka as, M. (2015). The
p edic ion capabili ies o bank up cy models
in a di e en en i onmne : an example o he
Al man Model unde he condi ions in he
Viseg ad g oup coun ies. Ekonomický časopis,
63(6), 617–633.
Schön eld, J., Kuděj, M., & Sm čka,
L. (2018). Financial heal h o en e p ises
in oducing sa egua d p ocedu e based on
bank up cy models. Jou nal o Business
Economics and Managemen , 19(5), 692–705.
h ps://doi.o g/10.3846/jbem.2018.7063
Singla, A., Sing Ahuja, I., & Sing Se hi, A.
(2017). Compa a i e Analysis o Technology
Push S a egies In luencing Sus ainable
De elopmen in Manu ac u ing Indus ies
Using Topsis and Viko Technique. In e na ional
Jou nal o Quali y Resea ch, 12(1), 129–146.
h ps://doi.o g/10.18421/IJQR12.01-08
Šo ánko á, B., Kiseľáko á, D., &
Ho á ho á, J. (2017). Ac ual ques ions o isk
managemen in models a ec ing en e p ise
pe o mance. Ekonomický časopis, 65(7),
644–667.
164 2021, XXIV, 1
Finance
S eimikiene, D., Balezen is, T.,
K isciukai iene I., & Balezen is, A. (2012).
P io i izing sus ainable elec ici y p oduc ion
echnologies: MCDM app oach. Renewable
& Sus ainable Ene gy Re iews, 16(5), 3302–
3311. h ps://doi.o g/10.1016/j. se .2012.02.067
Sude , A., & Kah aman, C. (2018).
Mul ia ibu e e alua ion o o ganic and
ino ganic ag icul u al ood in es men s using
uzzy TOPSIS. Technological and Economic
De elopmen o Economy, 24(3), 844–858.
h ps://doi.o g/10.3846/20294913.2016.1216905.
Sulub, S. A. (2014). Tes ing he p edic i e
powe o Al man’s e ised Z-model: The case o
10 mul ina ional companies. Resea ch Jou nal
o Finance and Accoun ing, 5(21), 174–184.
Sun, J., Li, H., Huang, Q. H., & He, K.
Y. (2014). P edic ing inancial dis ess and
co po a e ailu e: a e iew om he s a e-o -
he-a de ini ions, modeling, sampling, and
ea u ing app oaches. Knowledge-Based
Sys ems, 57, 41–56. h p://doi.o g/10.1016/j.
knosys.2013.12.006
Sušický, J. (2011). Využi elnos bank o ních
modelů a jejich aplikace podmínkách České
Republiky. P ague: Czech Uni e si y o Li e
Sciences P ague.
Sů o á, H., & Knai l, O. (2008). Finanční
analýza I. P ague: Ambis College.
Valáško á, K., Klieš ik, T., & Ko áčo á,
M. (2018). Managemen o inancial isks in
Slo ak en e p ises using eg ession analysis.
Oeconomia Cope nicana, 9(1), 105–121.
h ps://doi.o g/10.24136/oc.2018.006
Valáško a, K., Klieš ik, T., Š abo á, L., &
Adamko, P. (2018). Financial Risk Measu emen
and P edic ion Modelling o Sus ainable
De elopmen o Business En i ies Using
Reg ession Analysis. Sus ainabili y, 10(7),
1–15. h ps://doi.o g/10.3390/su10072144
Va ek, R. (2019). E alua ion o he Impac
o Selec ed Weigh ing Me hods on he Resul s
o he TOPSIS Technique. In e na ional Jou nal
o In o ma ion Technology & Decision Making,
18(6), 1821–1843. h ps://doi.o g/10.1142/
S021962201950041X
Va ek, R., & Cho anco á, J. (2019).
Assessmen o economic and en i onmen al
ene gy pe o mance o EU coun ies using
CV-TOPSIS echnique. Ecological Indica o s,
106, 105519. h ps://doi.o g/10.1016/j.
ecolind.2019.105519
Va ek, R., & Bečica, J. (2017). Capi al Ci y
as a Fac o o Mul i-C i e ia Decision Analysis
– Applica ion on T anspo Companies in he
Czech Republic. Ma hema ics, 8(10), 1765.
h p://doi.o g/10.3390/ma h8101765
Yalcin, N., & Ünlü, U. (2018). A Mul i-C i e ia
Pe o mance Analysis o Ini ial Public O e ing
(IPO) Fi ms Using C i ic and Viko Me hods.
Technological and Economic De elopmen o
Economy, 24(2), 534–560. h ps://doi.o g/10.38
46/20294913.2016.1213201
Yi, W. (2012). Z-sco e Model on Financial C isis
Ea ly Wa ning o Lis ed Real Es a e Companies
in China: A Financial Enginee ing Pe spec i e.
Sys ems Enginee ing P ocedia, 3, 153–157.
h ps://doi.o g/10.1016/j.sep o.2011.11.021
Yoon, K. (1980). Sys ems selec ion by
mul iple a ibu e decision making. Manha an,
KS: Kansas S a e Uni e si y.
Zalai, K. e al. (2013). Finančno-ekonomická
analýza podniku. B a isla a: Sp in 2.
Za adskas, E. K., Ma dani, A., Tu skis,
Z., Jusoh A., & No , K. (2016). De elopmen
o TOPSIS Me hod o Sol e Complica ed
Decision-Making P oblems: An O e iew
on De elopmen s. F om 2000 o 2015.
In e na ional Jou nal o In o ma ion Technology
& Decision Making, 15(03), 1–38. h p://doi.
o g/10.1142/S0219622016300019
Za adskas, E. K., Tu skis, Z., & Kildienė,
S. (2014). S a e o a su eys o o e iews
on MCDM/MADM me hods. Technological and
Economic De elopmen o Economy, 20(1),
165–179. h ps://doi.o g/10.3846/20294913.20
14.892037
Zelenko , Y., Fedo o a, E., & Chek izo , D.
(2017). Two-s ep classi ica ion me hod based
on gene ic algo i hm o bank up cy o ecas ing.
Expe Sys ems wi h Applica ions, 88, 393–401.
h ps://doi.o g/10.1016/j.eswa.2017.07.025
Zwingli, J., & Whi e, T. (2010). Can you
us you c edi model? C edi and Financial
Managemen Re iew, 16(2), 33–42.