Economic Modelling 43 (2014) 30–37

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Economic Modelling

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Analysis of the financial parameters of Serbian banks through theapplication of the fuzzy AHP and TOPSIS methods

Ksenija Mandic ⁎, Boris Delibasic 1, Snezana Knezevic 2, Sladjana Benkovic 3

University of Belgrade, Faculty of Organizational Sciences, Jove Ilica 154, Belgrade, Serbia

⁎ Corresponding author. Tel.: +381 11 260 77 66, +3260 77 60.

E-mail addresses: ksenija.mandic@crony.rs (K. Mandic(B. Delibasic), knezevic.snezana@fon.bg.ac.rs (S. Knezevic)(S. Benkovic).

1 Tel.: +381 11 395 08 23.2 Tel.: +381 69 889 34 54.3 Tel.: +381 11 395 08 71.

http://dx.doi.org/10.1016/j.econmod.2014.07.0360264-9993/© 2014 Elsevier B.V. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Accepted 31 July 2014Available online xxxx

Keywords:Serbian banking sectorFinancial performanceFuzzy logicMulti-criteria decision-making methodsFAHPTOPSIS

Banks represent entities of the financial market and the overall system for financing of the economy, i.e. they aredirectly or indirectly becoming the drivers and controlmechanismof thefinancial systemwithoutwhich the pro-cess of reproduction would be practically impossible. Banks, as specific financial institutions, hold a central placewithin thefinancial systemdue to the functions they perform, aswell as the relative volumeof financial potentialthat resides within their accounts. Evaluation of the work of banks is of essential importance to creditors, inves-tors and other interested parties, because it determines a bank's ability to be competitive within the sector. Theaim of this study is to propose a fuzzy multi-criteria model that will facilitate the assessment of the financial per-formance of banks. An analysiswas performed of the entire banking sector in Serbia covering the period betweenthe years 2005 and 2010. Methods such as the Fuzzy Analytic Hierarchy Process (FAHP) and the Technique forOrder Performance by Similarity to Ideal Solution (TOPSIS) have been integrated into the proposed model. Inthe first phase, we determined the priority weights of criteria using FAHP, while in the second phase we per-formed a ranking of the banks through the application of the TOPSIS method.

© 2014 Elsevier B.V. All rights reserved.

1. Introduction

In banking, as in many other industries, a business reputation is es-pecially important and has a significant effect on overall financial per-formance. The biggest threat to any bank, regardless of the scope of itspresence on a particular market, is the loss of business reputation. Thesecurity of a bank is a basic prerequisite for the obtainment and preser-vation of its long-term reputation within the public. One of the param-eters of a bank’s security is its assets, i.e. the assets it has at its disposal.Themajor role of this parameter is in the performance of business activ-ities and the realization of target performance in terms of profitability,solvency and liquidity.

Since the year 2001, the banking sector in Serbia has undergonemajor changes in conditions of an intensified process of economictransition. Banks owned by foreign entities account for 74% of the totalassets of the Serbian banking sector, and just as much of its capital. Atthe same time, foreign banks employ 20,564 people, which is 70.6% ofthe total 29,117 employees working in the banking sector in Serbia.

81 64 826 44 33; fax: +381 11

), boris.delibasic@fon.bg.ac.rs, benkovic.sladjana@fon.bg.ac.rs

The Serbian banking sector is heavily dependent on foreign banks, pri-marily from countries of the European Union which has been for a longtime now shaken by the debt crisis which negative consequences are al-ready being felt, whereby any further deepening of the crisis would haveeven stronger negative effects on the domestic banking sector. The acuteproblem of the Serbian banking sector is the significant share of non-performing loans, whichmakes it especially important to possess adequatemetrics for the effective management of financial performance (Bulajicet al., 2012). Furthermore, the banking sector in Serbia is characterized bya high level of competition i.e. a low level of concentration bearing inmind the large number of bankswith a lowparticipation in themost signif-icant categories of banking operations, such as: assets, loans, deposits, inter-est income, income from fees and commissions, and similar.

In the financial service sector, especially when it comes to bankingactivities, there is an increasing need for measuring performance. Dueto increased uncertainty and competition in the global bankingmarkets,measuring performance using fuzzy techniques provides clear andreliable information. The main objective of this study is to providedecision-making support, by enabling the decision-makers to measurethe effectiveness of banks through the application of multi-criteriadecision-making. In this regard, the paper proposes amodel for evaluat-ing the banking system's performance, which combines two multi-criteria methods: Fuzzy Analytic Hierarchy Process (FAHP) and theTechnique for Order Performance by Similarity to Ideal Solution(TOPSIS). The FAHP method is used to determine the priority weightsof the criteria, which are then used as the input weights of the criteria

31K. Mandic et al. / Economic Modelling 43 (2014) 30–37

for the TOPSIS method, whose application allows for ranking of thebanks.

The paper is organized in the following manner: the following sec-tion provides a brief review of the literature. Section 3 indicates thebasic starting points of fuzzy set theory and extended fuzzy AHP analy-sis, while Section 4 presents the TOPSIS method. Section 5 presents theintegrated fuzzy AHP — TOPSIS model for evaluating the financial pa-rameters of the Serbian banking sector. The paper ends with the con-cluding remarks which are given in Section 6.

2. Review of the literature

In the literature, many authors have used multi-criteria decision-making methods to evaluate the financial performance of the bankingsector. The method that has in numerous studies been recognized as auseful and systematic tool for measuring bank performance is theAnalytic Hierarchy Process — AHP (Saaty, 1980). In their study, Ta andKar (2000) used the AHP approach to make a selection of banks inSingapore. Frei andHarker (1999) applied theAHPapproach as an alter-native to the DEA method in order to measure bank performance andexplore the relationship between financial and operational perfor-mance. Yurdakul and Iç (2004) applied the AHP method to investigatethe credibility of companieswhich is necessary in bilateral relationshipsbetween production companies and banks in Turkey.

However, the AHPmethod is often criticized in the literature for fail-ing to take into account risks and uncertainties during the process ofevaluation (Chan et al., 2008; Dyer et al., 1992). Although AHP hasfoundwide application for solvingmulti-criteria decision-making prob-lems in real situations, this approach fails to provide satisfactory resultsin situations that can be characterized as uncertain. A lot of informationcannot be expressed by numbers. Ideally, the information should beprecise, certain, exhaustive and unequivocal. But in reality, it is oftennecessary to use information which does not have those characteristicsand hence there is a need to face the uncertainty of a stochastic and/orfuzzy nature (Munda et al., 1995). Furthermore, the criteria are oftenof a subjective and qualitative nature, which has a negative impact onthe decision-maker in terms of expressing his own references in numer-ical values and the subsequent comparison of the estimates (Chan andKumar, 2007). This is precisely what has led researchers to propose afuzzy version of the AHPmethod, which has been adapted to situationsof risks and uncertainty (Bottani and Rizzi, 2005; Chan et al., 2008;Mikhailov, 2002). A fuzzy assessment in the decision making processis very useful for the purpose of compensating for the above mentionedshortcoming of the AHP method.

There are many articles which use fuzzy approach tomeasure finan-cial parameters in the banking sector. For example, Ishizaka andNguyen(2013) used fuzzy AHPmethod to facilitate selection of student bank ac-counts. Also, Weifeng and Huihuan (2008) used the same method toevaluate the performances of commercial banks. Chen et al. (2013) ap-plied the fuzzy DEA method to analyze banking operations and marketrisk in Taiwan. Che et al. (2010), on the other hand, was using fuzzy AHPand DEA methods to assist in decision making when it comes to thechoice of bank loans for small and medium enterprises in Taiwan.

The authors who have applied similar methods to analyze banks asexplored in this paper are: Seçme et al. (2009) measured financialperformance of banks operating in Turkey. For this purpose he usedfuzzy AHP and TOPSIS methods. The same methods were used byMahrooz et al. (2013) to evaluate the performance of Iranian banks.Similarly, Akkoç and Vatansever (2013) proposed fuzzy AHP and fuzzyTOPSIS model to analyze Turkish banking sector, after the global finan-cial crisis.

3. Fuzzy set theory

The theory of fuzzy sets was presented by Zadeh (1965) as aneffective method for mathematical representation of uncertain and

imprecise evaluationsmade by humans. Human assessments are gener-ally characterized by imprecise language, such as the terms “equal”,“weak”, “fairly strong”, “very strong” and “absolute”. Therefore, the ap-plication of the fuzzy theory by decision-makers enables them to suc-cessfully deal with uncertainties. Furthermore, fuzzy logic can be thebasis for numerous methods through which qualitative assessmentscan be expressed through quantitative data.

That makes fuzzy set theory a more efficient approach compared toclassical (binary) set theory is its ability to reflect the real world(Ertugrul and Tus, 2007). Fuzzy set theory is applicable for the analysisof the same category of issues as classical theory. It is the most suitabletechnique for synthesis, whenever study findings contain a clear com-ponent of linguistic in terms of imprecise measurement (Nijkampet al., 2008). Fuzzy set theory is based on fuzzy sets which represent aclass of objects with a degree of membership (Negoita, 1985). Suchsets are characterized by a function of membership which is assignedto each object of the class with a rank that moves within the interval[0,1]. Themathematical operations that are allowed on the sets are: ad-dition, subtraction, multiplication and division (Dubois and Prade,1987; Kauffmann and Gupta, 1991).

A thorough analysis of fuzzy set theory was given by Zimmermann(1991). Bellman and Zadeh (1970) were the first to introduce the theo-ry of fuzzy sets into the decision-making process, and moreover in situ-ationswhen vague, imprecise and uncertain data were used to generatea decision. Yager and Basson (1975) had proposed the introduction offuzzy set theory into solving of the decision-making problem. In addi-tion to the above mentioned authors, others who have dealt with thisissue within their work are Zimmermann (1996); Lootsma (1997);Klir and Yuan (1995); and Kahraman et al. (2006).

3.1. Fuzzy AHP method (fuzzy analytic hierarchy process)

The fuzzy AHP method (Fuzzy Analytic Hierarchy Process — FAHP)has been suggested by various authors (Buckley, 1985; Chang, 1996;Mikhailov and Tsvetinov, 2004; Van Laarhoven and Pedrcyz, 1983).FAHP represents a systematic approach to selecting alternatives andsolving problems using the concept of fuzzy set theory (Zadeh, 1965)and the AHPmethod, which are implemented through the use of trian-gular fuzzy numbers (Chang, 1996). Triangular fuzzy numbers are ap-plied in order to determine the priority of different decision variables,while the extended AHP method is used to determine the final priorityof weights based on triangular fuzzy numbers. The most commonlyused is the FAHP methodology which was extensively analyzed byChang (1992, 1996).

Let X={x1, x2,…, xn} be a set of objects, and let G={g1, g2,…, gn} bea set of goals. According to themethodology of extended analysis whichwas set up by Chang (1992, 1996), an extended analysis of goal gi is per-formed for every taken object. The values of extended analysis m foreach object can be represented as follows:

M1gi; M

2gi; …; Mn

gi; i ¼ 1;2;…;n; ð1Þ

whereMgij (j=1, 2,…,m) are fuzzy triangular numbers. Chang's extend-

ed analysis consists of the following steps:

Step 1. The values of fuzzy extensions for the i-th object are given inExpression (2):

Si ¼Xm

j¼1Mj

gi⊗Xn

i¼1

Xmj¼1

Mjgi

h i−1: ð2Þ

In order to obtain the expression [∑i = 1n ∑ j = 1

m Mgij ]−1, it is neces-

sary to perform additional fuzzy operations with m values of the ex-tended analysis, which is represented by Expressions (3) and (4):

Xmj¼1

Mjgi ¼

Xmj¼1

liXm

j¼1mi

Xmj¼1

uiÞ;�

ð3Þ

1

dl1l2 M

D

u2 um1m2

V (M2 ≥ M1)

M2

MM

M1

Fig. 1. The intersection between M1 andM2.

Table 1Linguistic scale of importance.

Linguistic scale ofimportance

Triangular fuzzynumbers

Reciprocal value of triangularfuzzy numbers

Equal (1,1,1) (1,1,1)Weak (1/2,1,3/2) (2/3,1,2)Fairly strong (3/2,2,5/2) (1/2,1,3/2)Very strong (5/2,3,7/2) (2/7,1/3,2/5)Absolute (7/2,4,9/2) (2/9,1/4,2/7)

32 K. Mandic et al. / Economic Modelling 43 (2014) 30–37

Xni¼1

Xmj¼1

Mjgi ¼

Xnj¼1

liXn

j¼1mi

Xnj¼1

ui

� �: ð4Þ

In other words, it is necessary to calculate the inverse vector usingExpression (5):

Xni¼1

Xmj¼1

Mjgi

h i−1 ¼ 1Xni¼1

ui

;1Xni¼1

mi

;1Xni¼1

li

!: ð5Þ

Step 2. The degree of possibility forM2 = (l2,m2, u2) andM1 = (l1,m1,u1) is defined by Expression (6):

V M2≥M1ð Þ ¼ y≥x min μM1 xð Þ; μM2 yð Þð Þ½ � : ð6Þ

It can be represented in the following manner by Expression (7):

V M2≥M1ð Þ ¼ hgt M1 ∩M2ð Þ ¼ μM2 dð Þ;

¼1 ; if m2 ≥ m10; i f l1 ≥ u2l1−u2

m2− u2ð Þ− m1− l1ð Þ ; otherwise;

8>><>>:

ð7Þ

Table 2Fuzzy comparison matrix of the eight basic criteria in relation to the goal and their priority vec

Criteria Equity Portfolio Sources Liquid assets C

Equity (1,1,1) (1,1,1) (1/2,1,3/2) (3/2,2,5/2) (Portfolio (1,1,1) (1,1,1) (1,1,1) (1,1,1) (Sources (2/3,1,2) (1,1,1) (1,1,1) (1,1,1) (Liquid assets (2/5,1/2,2/3) (1,1,1) (1,1,1) (1,1,1) (Cash (1,1,1) (1,1,1) (1,1,1) (2/3,1,2) (NII+ (1,1,1) (1,1,1) (1,1,1) (1,1,1) (CBNI+ (1,1,1) (1,1,1) (1,1,1) (1,1,1) (EBT (1,1,1) (1,1,1) (1,1,1) (1,1,1) (

where d is the ordinate of the highest intersection point D between μM1

and μM2 (Fig. 1).In order to compare M1 and M2, values of both V (M1 ≥ M2) and

V(M2 ≥ M1) are needed.

Step 3. The degree of possibility for a convex fuzzy number to begreater than the k convex numbers Mi (i = 1, 2, …, k) can be definedby Expression (8):

V M ≥ M1; M2;…; Mkð Þ¼ V M ≥ M1ð Þ i M ≥ M2ð Þ i… i M ≥ Mkð Þ½ �¼ minV M ≥ Mið Þ; i ¼ 1;2;3;…; k: ð8Þ

Let us assume that Expression (9) is true:

d0 Aið Þ ¼ min V Si ≥ Skð Þ ð9Þ

for k = 1, 2, … n; k ≠ i. The weight vector is obtained by Expression(10):

W 0 ¼ d0 A1ð Þ; d0 A2ð Þ;…; d0 Anð Þ� �T ð10Þ

where Ai (i = 1, 2, …, n) consists of n elements.

Step 4. Through normalization, the weight vectors are reduced to Ex-pression (11):

W ¼ d A1ð Þ; d A2ð Þ;…; d Anð Þð ÞT ð11Þ

where W does not represent a fuzzy number (Büyüközkan et al., 2008;Kahraman et al., 2006).

4. TOPSISmethod (technique for order performance by similarity toideal solution)

TOPSIS represents a classical multi-criteria decision-makingmethod. This method ranks alternatives according to their distancefrom the so-called positive ideal solution (PIS) and negative ideal so-lution (NIS). PIS represents a solution that maximizes the benefitcriteria and minimizes the cost criteria, while NIS has the oppositelogic, i.e. it maximizes the cost criteria and minimizes the benefitcriteria (Benitez et al., 2007). The TOPSIS method takes into accountboth PIS and NIS distances, whereby the optimal alternative is theone that is in geometric terms the closest to PIS, and the farthestfrom NIS (Seçme et al., 2009). The ranking of alternatives is basedon the relative similarity to the ideal solution, which avoids the situ-ation of the alternative having the same similarity to both PIS andNIS.

The PIS is defined using the best rating of the values of thealternatives for each individual criterion; conversely, the NISrepresents the worst values of the alternatives' ratings. The terms“best” and “worst” are interpreted for each criterion separately,according to whether maximization or minimization of criteria isin question.

tors.

ash NII+ CBNI+ EBT Priority vector (Wc)

1,1,1) (1,1,1) (1,1,1) (1,1,1) 0,2460281,1,1) (1,1,1) (1,1,1) (1,1,1) 0,0703391,1,1) (1,1,1) (1,1,1) (1,1,1) 0,1454641/2,1,3/2) (1,1,1) (1,1,1) (1,1,1) 0,0681511,1,1) (1,1,1) (1,1,1) (1,1,1) 0,1454641,1,1) (1,1,1) (1,1,1) (2/5,1/2,2/3) 0,0081871,1,1) (1,1,1) (1,1,1) (1,1,1) 0,0703381,1,1) (3/2,2,5/2) (1,1,1) (1,1,1) 0,246029

Table 3Values of the basic financial criteria of banks for the year 2005.

Equity (0,246) Portfolio (0,070) Sources (0,145) Liquid ass. (0,068) Cash (0,145) NII+ (0,008) CBNI+ (0,070) EBT (0,246)

KBC banka 4.674.248,00 7.529.267,00 5.484.645,00 2.489.656,00 1.996.988,00 −1.216.203,00 −616.461,00 266.687,00Agrobanka 7.575.127,00 33.554.503,00 37.309.083,00 4.831.266,00 3.478.618,00 −3.683.433,00 −2.856.436,00 −804.955,00AIK banka 43.815.850,00 65.750.619,00 32.698.091,00 9.113.789,00 7.503.246,00 −19.887.113,00 −18.358.174,00 5.485.859,00Alpha bank 30.215.095,00 50.955.454,00 45.972.489,00 10.936.589,00 5.331.921,00 −2.812.523,00 −1.231.497,00 93.597,00Piraeus bank 4.647.179,00 17.838.357,00 18.757.681,00 6.738.577,00 4.538.342,00 −98.070,00 419.826,00 220.217,00Cacanska banka 5.917.898,00 8.854.011,00 6.105.806,00 1.839.556,00 1.422.617,00 541.845,00 954.437,00 384.678,00Marfin bank 5.963.314,00 19.689.686,00 19.283.472,00 4.647.057,00 3.235.310,00 −1.286.385,00 −532.271,00 223.486,00NLB banka 13.719.829,00 34.750.365,00 32.745.389,00 8.834.345,00 5.797.981,00 317.759,00 1.534.179,00 624.950,00Credy banka 4.424.473,00 7.183.281,00 8.564.107,00 4.003.597,00 3.536.943,00 −3.392.499,00 −2.785.631,00 −105.897,00Banca Intesa 41.002.983,00 211.852.222,00 228.401.370,00 63.269.715,00 36.909.066,00 −2.157.920,00 3.576.260,00 4.785.404,00EFG Eurobank 7.003.188,00 33.781.801,00 30.273.495,00 5.026.643,00 1.581.784,00 −260.635,00 214.976,00 −2.493.887,00UniCredit bank 9.560.485,00 99.404.007,00 99.711.669,00 24.122.515,00 6.511.772,00 516.278,00 1.474.817,00 989.864,00Hypo-Alpe 21.410.568,00 163.851.518,00 161.774.652,00 32.131.001,00 7.921.379,00 −16.768.708,00 −15.521.895,00 2.409.257,00JUBMES banka 7.621.709,00 11.568.424,00 6.265.952,00 1.648.327,00 738.197,00 311.186,00 481.141,00 265.863,00Jugobanka 3.557.363,00 27.026.669,00 24.422.333,00 121.837,00 121.837,00 −396.513,00 −378.651,00 94.519,00Komercijalna 28.382.304,00 198.332.100,00 218.980.414,00 62.210.242,00 39.310.649,00 −1.271.374,00 3.994.981,00 677.924,00Dunav banka 916.579,00 420.847,00 566.887,00 484.166,00 480.308,00 7.264,00 79.274,00 59.849,00OTP banka 21.342.365,00 32.671.822,00 19.946.407,00 4.812.523,00 3.201.711,00 −7.761.745,00 −6.877.686,00 1.759.094,00Credit Agricole 10.705.436,00 25.781.518,00 23.332.265,00 6.158.998,00 3.992.141,00 382.896,00 1.682.748,00 1.167.178,00RB Vojvodine 9.060.688,00 10.339.435,00 10.155.445,00 4.872.842,00 4.142.965,00 414.177,00 912.582,00 568.972,00Moskovska 0 0 0 0 0 0 0 0Findomestic 3.996.221,00 7.009.978,00 6.691.430,00 3.270.374,00 2.210.340,00 218.363,00 560.534,00 32.261,00Erste bank 7.932.994,00 34.341.662,00 32.945.526,00 6.873.829,00 3.490.147,00 −955.949,00 −227.855,00 −491.417,00Opportunity 0 0 0 0 0 0 0 0PB Beograd 4.095.663,00 10.615.582,00 12.941.839,00 6.644.800,00 5.534.790,00 −268.577,00 109.796,00 66.171,00PB Pancevo 11.382.415,00 14.909.441,00 5.727.505,00 2.315.389,00 1.877.914,00 −3.158.295,00 −2.843.887,00 1.411.330,00Postanska sted. 6.450.450,00 32.848.419,00 40.326.171,00 17.744.272,00 15.097.894,00 1.038.158,00 4.664.459,00 280.641,00ProCredit bank 7.048.894,00 68.331.421,00 64.414.698,00 9.464.816,00 2.356.745,00 3.279.224,00 4.315.318,00 1.219.485,00Raiffeisenbank 25.360.453,00 348.049.568,00 333.021.604,00 64.441.263,00 13.904.384,00 −5.482.492,00 −3.853.019,00 1.426.161,00Societe Generale 11.997.847,00 104.284.608,00 99.045.156,00 22.838.242,00 6.837.662,00 1.021.356,00 2.898.158,00 −114.687,00Srpska banka 9.740.857,00 27.004.849,00 23.122.051,00 7.877.240,00 3.911.693,00 −2.013.669,00 −1.682.436,00 453.580,00Univerzal banka 6.127.969,00 12.354.397,00 11.518.498,00 4.375.872,00 2.679.306,00 −1.749.839,00 −934.684,00 428.914,00Vojvodjanska 17.060.041,00 113.646.955,00 123.374.586,00 21.105.366,00 12.704.755,00 −16.212.025,00 −13.383.155,00 −3.731.307,00Volks banka 3.686.314,00 27.631.966,00 28.186.251,00 7.150.754,00 2.734.363,00 −1.550.894,00 −1.454.733,00 −1.243.481,00

Table 4PIS, NIS, Cci and the ranking of banks for the year 2005.

d+ d- Cci RANK

KBC banka 0,216723242 0,109511771 0,335683683 23Agrobanka 0,226863521 0,084497405 0,271380889 30AIK banka 0,125720676 0,253811464 0,668748275 2Alpha bank 0,186352279 0,125280929 0,402014053 12Piraeus bank 0,213610115 0,109819603 0,339547037 21Čacanska banka 0,213648908 0,113843999 0,347622792 19Marfin bank 0,21311605 0,109107287 0,33860765 22NLB banka 0,193449347 0,123867545 0,390359127 13Credy banka 0,221671041 0,099125381 0,308997776 28Banca Intesa 0,049231314 0,261844664 0,841738619 1EFG Eurobank 0,260601911 0,05542685 0,175385462 33UniCredit bank 0,18373107 0,133574643 0,420965137 8Hypo-Alpe-Adria bank 0,146460401 0,170205576 0,537492462 6JUBMES banka 0,214011223 0,111121134 0,341771994 20Jugobanka Jugbanka 0,220275959 0,10566993 0,324194701 25Komercijalna banka 0,140834484 0,175279422 0,554481846 4Dunav banka 0,226454203 0,104883113 0,316544826 27OTP banka 0,17399469 0,149238755 0,461705796 7Credit Agricole bank 0,191530444 0,134565 0,41265526 11RB Vojvodine 0,204199907 0,119318252 0,368814699 15Moskovska banka 0 0 0 34Findomestic bank 0,220756579 0,105046898 0,322424116 26Erste bank 0,22077257 0,094111351 0,298876332 29Opportunity banka 0 0 0 35PB Beograd 0,216754262 0,106045945 0,328518826 24PB Pancevo 0,192207941 0,137143887 0,416405423 10Postanska stedionica 0,200132449 0,120341299 0,37551063 14ProCredit bank 0,191591996 0,137748415 0,418255431 9Raiffeisenbank 0,136717138 0,178688037 0,566534894 3Societe Generale 0,199120408 0,11180999 0,35959813 17Srpska banka 0,203842008 0,114964347 0,360608706 16Univerzal banka 0,211122554 0,113465895 0,349568492 18Vojvodjanska banka 0,266904691 0,058836365 0,180623118 32Volks banka 0,240046507 0,074911042 0,237844885 31Other 0,146459475 0,18127907 0,553120994 5

33K. Mandic et al. / Economic Modelling 43 (2014) 30–37

The TOPSIS methodology presented by Hwang and Yoon (1981)consists of the following steps:

Step 1. The decision matrix is normalized through the application ofExpression (12):

rij ¼WijffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX Jj¼1

W2ij

q ; j ¼ 1;2;…; J; i ¼ 1;2;…n : ð12Þ

Step 2. Aweighted normalized decisionmatrix is obtained bymultiply-ing the normalized matrix with the weights of the criteria, Expression(13):

Vij ¼ W�i rij; j ¼ 1;2;…; j; i ¼ 1;2;…;n: ð13Þ

Step 3. PIS (maximum value) and NIS (minimum value) are deter-mined by Expressions (14, 15):

A� ¼ V�1;V

�2;…;V�

n

� � ð14Þ

A− ¼ V−1 ;V−

2 ;…;V−nf g: ð15Þ

Step 4. The distance of each alternative from PIS and NIS is calculatedusing Expressions (16) and (17):

d�i ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXnj¼1

Vij−V�j

� �2;

vuut j ¼ 1;2;…; J ð16Þ

Table 5CCi and ranking of the banks for the period between the years 2005 and 2010.

Name of bank Cci RANK(2005)

Cci RANK(2006)

Cci RANK(2007)

Cci RANK(2008)

Cci RANK(2009)

Cci RANK(2010)

KBC banka 0,335684 23 0,358353 24 0,230796 32 0,1063141 30 0,22135 23 0,126872 24Agrobanka 0,271381 30 0,394897 16 0,190501 33 0,2828088 12 0,37753 9 0,265953 9AIK banka 0,668748 2 0,688569 2 0,72427 3 0,5953392 3 0,65557 3 0,617861 2Alpha bank 0,402014 12 0,371283 21 0,331085 14 0,2561488 14 0,14185 33 0,133351 21Piraeus bank 0,339547 21 0,290256 30 0,244221 28 0,1720269 20 0,21693 26 0,15412 18Čacanska 0,347623 19 0,382154 18 0,301378 18 0,1566312 21 0,24879 17 0,134682 20Marfin bank 0,338608 22 0,300769 29 0,238004 30 0,0957746 31 0,20132 30 0,128687 23NLB banka 0,390359 13 0,380433 19 0,312133 17 0,177493 19 0,20824 29 0,159562 16Credy banka 0,308998 28 0,343982 26 0,24331 29 0,0836952 35 0,20973 28 0,080211 32Banca Intesa 0,841739 1 0,699706 1 0,809208 1 0,8927901 1 0,93007 1 0,828637 1EFG Eurobank 0,175385 33 0,247735 31 0,507668 9 0,5764243 5 0,55091 5 0,441258 6UniCredit bank 0,420965 8 0,530486 5 0,530253 7 0,4550584 7 0,52755 6 0,490077 5Hypo-Alpe-Adria bank 0,537492 6 0,417701 10 0,576146 6 0,479585 6 0,50275 7 0,329432 7JUBMES banka 0,341772 20 0,401175 14 0,292379 19 0,2936939 10 0,25949 16 0,137401 19Jugobanka Jugbanka 0,324195 25 0,345801 25 0,245916 25 0,1231779 26 0,23296 18 0,120906 26Komercijalna banka 0,554482 4 0,661424 3 0,654534 4 0,5951755 4 0,57328 4 0,569373 4Dunav banka 0,316545 27 0,340634 27 0,24471 27 0,1214306 27 0,23026 20 0,119363 28OTP banka 0,461706 7 0,543386 4 0,367914 11 0,2751134 13 0,1776 31 0,071776 34Credit Agricole 0,412655 11 0,379281 20 0,186012 34 0,0942277 32 0,16378 32 0,0777 33RB Vojvodine 0,368815 15 0,389592 17 0,330121 15 0,0860376 34 0,21782 25 0,15431 17Moskovska banka 0 0 0 0 0 0 0,115923 29 0,21931 24 0,105551 30Findomestic bank 0,322424 26 0,317945 28 0,235098 31 0,1272601 24 0,21233 27 0,093711 31Erste bank 0,298876 29 0,160257 33 0,274971 20 0,2116534 18 0,30797 14 0,174061 14Opportunity banka 0 0 0 0 0,246497 24 0,1244224 25 0,22264 22 0,106763 29PB Beograd 0,328519 24 0,36517 23 0,267273 22 0,1379485 22 0,22902 21 0,126023 25PB Pancevo 0,416405 10 0,408441 12 0,25751 23 0,0909802 33 0,08731 34 0,130498 22Postanska stedionica 0,375511 14 0,191283 32 0,245045 26 0,2457982 16 0,3231 13 0,239131 11ProCredit bank 0,418255 9 0,414788 11 0,357745 12 0,2503135 15 0,35572 12 0,198393 13Raiffeisenbank 0,566535 3 0,502074 8 0,790307 2 0,8240243 2 0,73601 2 0,605873 3Societe Generale 0,359598 17 0,511213 6 0,514557 8 0,3757942 9 0,43428 8 0,317139 8Srpska banka 0,360609 16 0,401437 13 0,268177 21 0,1213522 28 0,23088 19 0,119835 27Univerzal banka 0,349568 18 0,401053 15 0,317054 16 0,2142491 17 0,26632 15 0,161351 15Vojvodjanska banka 0,180623 32 0,495024 9 0,597057 5 0,3825816 8 0,37377 10 0,209978 12Volks banka 0,237845 31 0,365598 22 0,357471 13 0,2869426 11 0,36513 11 0,264151 10Other 0,553121 5 0,509911 7 0,37442 10 0,1298973 23 0 0 0 0

34 K. Mandic et al. / Economic Modelling 43 (2014) 30–37

d−i ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXnj¼1

Vij−V−j

� �2;

vuut j ¼ 1;2;…; J: ð17Þ

Step 5. The closeness coefficient for each alternative (CCi) is calculatedby applying Expression (18):

CCi ¼d−i

d�i þ d−i: ð18Þ

Step 6. At the end of the analysis, the ranking of alternatives is madepossible by comparing the CCi values.

5. Application of the FAHP and TOPSIS methods in the evaluation ofthe financial parameters of the banking sector

The data taken into account for the modeling include the entirebanking sector in Serbia during the period between the year 2005 and2010. The study utilized the financial data for the 35 commercialbanks that are operating in Serbia. Eight criterions i.e. financial parame-ters were taken into consideration: Equity, Portfolio, Sources, Liquid As-sets, Cash, NII+, CBNI+, and EBT (Knezevic, 2011). The model wasconstructed by combining two methods of multi-criteria decision-making: the Fuzzy Analytic Hierarchy Process — FAHP and the Tech-nique for Order Performance by Similarity to Ideal Solution — TOPSIS.

The FAHPmethodology was applied first in order to allow for deter-mination of the weight vectors for each financial parameter individual-ly. The FAHP procedure can be represented on the basis of two phases:

Phase I. Defining of the basic criteria in relation to the goal. As the goalof the research, we identified the “Evaluation of the financial parame-ters of Serbian banks”. Eight criteria were analyzed: Equity, Portfolio,Sources, Liquid Assets, Cash, Net Interest Income, Core Business Net In-come and Earnings before Tax.

Movement of Equity criterion is the basis for evaluating the perfor-mance of banks. Portfolio includes callable deposits and loans, the in-terest and fees, given loans and deposits, securities and otherinvestments. The average portfolio taken in this paper as one of the pa-rameters is important because its use leads to generation of Net InterestIncome. Criterion Sources include average sources such as transactiondeposits, other deposits and borrowings, obligations under the securi-ties, obligations for interests, fees and the valuation of derivatives. Prop-er use of these sources of funding affects the profitability of the banks.Given the fact that banks, by their nature of activities, often take risksin business transactions, it is important when analyzing the efficiencyof banks to take into account the criterion of Liquid Assets. Cash (cashand cash equivalents) is themost liquid part of the assets, and also syn-thesized reflection of the impact of business activities of the bank instatement of cash flows (from operating activities and financing activi-ties and investing) on the amount of cash and cash equivalents. Net In-terest Income (NII+) represents the net income from interest less thanthe indirect write-offs. Interest income is one of the most importantbank's incomes. Core Business Income (CBNI+) is an important crite-rion that includes Net Interest Income and income from fees and com-missions net of indirect write-offs. Earning before tax (EBT) is a very

Table 6Total CCi and rank for the period between 2005 and 2010.

Name of bank Total Cci RANK

Banca Intesa 0,833692155 1Raiffeisenbank 0,670803959 2AIK banka 0,658393013 3Komercijalna banka 0,601378069 4Hypo-Alpe-Adria 0,473851354 5Societe Generale 0,418763283 6EFG Eurobank 0,416563994 7UniCredit bank 0,404473165 8Other 0,391837528 9Vojvodjanska banka 0,373172258 10ProCredit bank 0,332535497 11OTP banka 0,316249009 12Volks banka 0,312857073 13Agrobanka 0,297178727 14JUBMES banka 0,287651262 15Univerzal banka 0,284933096 16Alpha bank 0,272622801 17NLB banka 0,271369486 18Postanska sted. 0,269977282 19Cacanska banka 0,261875837 20RB Vojvodine 0,257781885 21Srpska banka 0,25038211 22PB Beograd 0,242325991 23Erste bank 0,237964109 24Piraeus bank 0,236183946 25Jugobanka 0,232158622 26PB Pancevo 0,231857911 27KBC banka 0,229895508 28Findomestic bank 0,21812771 29Marfin bank 0,217193866 30Credy banka 0,211654516 31CreditAgricole 0,203237234 32Dunav banka 0,190447007 33Opportunity banka 0,175079358 34Moskovska banka 0,146929394 35

35K. Mandic et al. / Economic Modelling 43 (2014) 30–37

important criterion for evaluating the performance of banks relative tothe invested capital. Also, this indicator is an indicator for measuringproductivity (EBT/average number of employees).

Phase II. The priority weights of each criterion are calculated by apply-ing the FAHP method. The comparison of criteria was made easier forthe experts by using a Linguistic scale of importance (Kilincci andOnal, 2011). As human speech is characterized by verbal expressions,it is natural to express people's attitudes by way of linguistic terms.Fuzzy AHP method uses a scale that is composed of linguistic variableswhose values are not numbers but words. Linguistic variables can bespecified and mapped to fuzzy numbers. In this case, we use a scale offive linguistic terms: Equally, Weak, Fairly Strong, Very Strong and Ab-solute (Table 1). When comparing linguistic criteria a financial expertselects a linguistic variable that best suits the importance of a particularcriteria. Then, each variable in the scale is mapped to a triangular fuzzynumber, which means that each variable is defined by three values.

Table 2 shows fuzzy comparison matrix for eight basic criteria.Table 2 shows that criterion Equity has weak significance against crite-rion Sources. Under the Equity we mean the bank's assets financed byown capital, and Sources are the bank's assets financed by their ownand external capital. Thus, in a given comparison Equity is a more im-portant indicator because it shows the true power of banks and is aguarantee for creditors. Compared with the criterion of Liquid AssetsEquity parameter has a fairly strong significance. Liquid assets are animportant indicator for the proper settlement of liabilities to creditors.Simultaneously, Equity is an important indicator of the efficiency ofthe use of funds by the bank's management. If we compare the criteriaLiquid Assets and Cash, Liquid Assets are more significant because it

is a broader concept. Also, from the table we can see that the parameterEBT has a fairly strong significance against criterion NII+. Themain rea-son is that EBT is a broader term that represents the synthesized indica-tor of income and expenditure while the NII+ only applies to incomeand interest expense.

It can be concluded that in the process of evaluation of the financialparameters of Serbian Banks, the criteria of Equity and EBT are themostsignificant with a weight vector of 0.246, followed by the criteria ofSources and Cash with a vector of 0.145, Portfolio and CBNI+ with avector of 0.070, Liquid Assets with 0.068 and NII+ with 0.08. Table 3provides a financial report with the real data for the year 2005 with cal-culated weight vectors for the criteria. Thirty five commercial bankswere taken into consideration, which constitute the entire banking sec-tor in Serbia.

After determining the weight vectors of the criteria using FAHP, wepropose the use of the TOPSIS method which allows for the ranking ofbanks based on the financial criteria. The first step in the TOPSIS calcu-lation is the normalization of the decision matrix (Table 3) throughthe use of Expression (12). The normalized matrix is then multipliedby the FAHPweight vectors of the criteria using Expression (13), the re-sult of which is a weighted normalized matrix.

The next stepwithin the TOPSISmethod is to determine the shortestdistance from the PIS using Expression (16), and the farthest distancefrom the NIS using Expression (17). Following the calculation of PISand NIS using Expression (18), it is possible to obtain the closeness co-efficient (CCi) for each alternative i.e. bank. Table 4 provides a completeoverview of the parameters PIS, NIS, CCi and the ranking of the banks.The TOPSIS method simultaneously considers both PIS and NIS dis-tances, so that eventually an ideal solution is obtained that is the closestto PIS and the farthest from NIS.

An identical procedure was applied to rank the banks for the years2006, 2007, 2008, 2009 and 2010. The obtained results are shown inthe summarized Table 5, in which we can see that Banca Intesa holdsthe best position for all of the observed years.

Aggregation of the results for the period between 2005 and 2010,which are given in Table 5, allowed for an insight into the overall rank-ing of the banks, which is shown in Table 6.

We can see from Table 6 that for the period between 2005 and 2010,Banca Intesa has the highest ranking taking into account all of thecriteria that were considered. It is followed by Raiffeisenbank, AIKBank, Commercial Bank, Hypo-Alpe-Adria bank, etc.

6. Conclusion

Bearing in mind the pronounced fragmentation of the bankingsector, we can expect a continuance of capital consolidation underthe influence of competition in the future, as well as other similartrends that are coming from abroad. Namely, further consolidationis expected within large banking groups in themarket, but also with-in the ranks of smaller banks that will be unable to withstand thepressure of competition with the big players (costs, insufficient ca-pacities, low economies of scale). Small banks will be forced to seekout a strategic partner, or a partner among the banks of its size oramong any of the major banks. In the future, the development ofbanking in Serbia will be significantly determined by the qualityand level of domestic savings. In the business conditions character-ized by the financial crisis, many banks will inevitably move to amodel of sustainable funding. In such circumstances, efficient man-agement of bank performance is of particular importance.

The measurement of bank performance is of key importance to theeconomy. The uncertainty and complexity of the global market, aswell as an increase in the flow of information, represent the greatest ob-stacles for accurate measurement of performance. In such conditions,traditional performance measurements fail to produce satisfactory re-sults. However, a fuzzy multi-criteria approach has been successfullyused to overcome this problem. Within the study, a model was

36 K. Mandic et al. / Economic Modelling 43 (2014) 30–37

constructed combining twomethods of multi-criteria decision-making:Fuzzy AHP and TOPSIS. In the first phase, the priority weights of thecriteria were determined using Fuzzy AHP, while in the second phasewe performed a ranking of the banks through the use of the TOPSISmethod.

Following the conducted research based on the selected financialcategories in the process of evaluation of the financial parameters ofSerbian banks, the criteria of Equity and EBT proved to be the most sig-nificantwith aweight vector of 0.246, followed by the criteria of Sourcesand Cash with a vector of 0.145, Portfolio and CBNI+ with a vector of0.070, Liquid Assets with a vector of 0.068 and NII+ with a vector of0.08. The results that were obtained in the study are not surprising.Namely, EBT is a particularly important financial indicator due to thefact that profitability is at the center of the business policies of allbanks, while Equity represents a risk buffer. Capital plays a very impor-tant role in the realization of a balance between risk and return, i.e. themain function of a bank's capital is to reduce the risk of the bank'soperations.

The banks were tested based on the selected financial indicators —Equity, Portfolio, Sources, Liquid Assets, Cash, Net Interest Income,Core Business Net Income and Earnings before Tax, and it wasobserved that Banca Intesa had the best rating among the observedranked banks.

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M.Sc. Ksenija Mandic received her BSc and MSc degrees inFaculty of Organizational Science from the University ofBelgrade, Serbia, in 2006 and 2008, respectively. She is cur-rently PhD student in the same faculty in the specializationof Management. She works in telecommunication company

Crony since 2007. Her main research interests include: deci-sionmaking theory,multi-criteria decision analysis, fuzzy settheory, optimization modeling.

Boris Delibasic is associate professor at University ofBelgrade's Faculty of Organizational Sciences in Serbia. He re-ceived his PhD in 2007. In 2012 he received the Fulbright Vis-iting Scholar grant and did his postdoctoral studies at theCenter for Data Analysis and Biomedical Informatics at Tem-ple University in Philadelphia, PA. He serves as coordinationboard assistant at the European Working Group on DecisionSupport Systems since 2011. His area of expertise are in thedomain of multi-attribute decision making, decision supportsystems, and data mining.

c Mo

Snezana Knezevic is associate professor at University ofBelgrade's Faculty of organizational Sciences in Serbia. Shegraduated from the Faculty of Economics in Belgrade whereshe also got her MSc degree. She got her PhD degree at theFaculty of Organizational Sciences in Belgrade. Area of inter-est: financial management, accounting and environmentalprotection.

K. Mandic et al. / Economi

Sladjana Benkovicworks as associate professor at the Facul-ty of Organizational Science, Belgrade University, Serbia,where she completed her bachelor, master and doctoralstudies. She has worked at the Faculty for the last 15 years,and her preferences regarding research and teaching inter-ests are related to the field of financial management,methods offinancing corporate development, project financ-ing, appraisal and evaluating of cash flow.

37delling 43 (2014) 30–37