Predicting Bankruptcies Using Rough Set

AMERICAN CONFERENCE ON APPLIED MATHEMATICS (MATH '08), Harvard, Massachusetts, USA, March 24-26, 2008

Predicting Bankruptcies Using Rough Set Approach: The Case of Turkish Banks NURSEL SELVER RUZGAR*, FAHRI UNSAL**, BAHADTIN RUZGAR*** *Vocational School of Social Sciences, Marmara University Beyazit Campus, Eminonu, Istanbul, TURKEY [email protected] **School of Business, Marketing/Law, Ithaca College 410 New Business Building, Ithaca, NY 14850 [email protected], http://faculty.ithaca.edu/unsal/ ***Banking and Insurance School, Actuaries Department, Marmara University Goztepe Campus, Kadikoy, 34722, Istanbul, TURKEY [email protected], http://mimoza.marmara.edu.tr/~bruzgar/ Abstract: - Evaluation of the reasons for business failures has been a major preoccupation of researchers and practitioners for many years. A large number of methods including multiple regression analysis, discriminant analysis, logit analysis, recursive partitioning algorithm, and several other techniques have been used for the prediction of business failures. This study has followed a different approach using the Rough Set theory to investigate the reasons of bankruptcies in the Turkish banking system. For this purpose, financial ratios of 29-41 commercial banks were examined for the 1995-2007 period. The results showed that this model is a promising alternative to the conventional methods for bankruptcy prediction. Key-Words: - Bankruptcy prediction, Financial ratios, Rough Set Theory, Classification some of these methods led to models with a satisfactory ability to discriminate between healthy and potentially risky (candidates for bankruptcy) businesses, they suffer from some limitations, often due to the unrealistic assumption of statistical hypotheses or due to a confusing language of communication with the decision makers [5]. In this paper, the Rough Set (RS) approach is used to provide a set of rules that are able to discriminate between healthy and failing banks in order to predict bank failures. Rough Set Theory (RST) was introduced by Pawlak [13]. The RS philosophy is based on the assumption that with every object of the universe there is associated a certain amount of information expressed by means of some attributes used for object description. Objects having the same description are indiscernible with respect to the available information. The indiscernibility relation thus generated constitutes a mathematical basis of the RST; it induces a partition of the universe into blocks of indiscernible objects, called elementary sets that can be used to build knowledge about a real or abstract world. The use of the indiscernibility relationship results in information granulation [14]. There are many potential applications in different fields [15]. In pharmacology, the analysis of relationships between the chemical structure and the antimicrobial activity of drugs [16] has been successfully investigated. Banking applications include

1 Introduction Business failure, according to a widespread definition, is the situation that a firm cannot pay lenders, preferred stock shareholders, suppliers, and hence goes into bankrupt according to the law. The number of failing firms is an important indicator of the health of the economy [1]. The high individual and social costs encountered in corporate bankruptcies make this decision problem very important to parties such as auditors, management, government policy makers, and investors. Bankruptcy is a worldwide problem and the number of bankruptcies can be considered an index of the robustness of individual country’s economy [2]. The bankruptcy literature reveals a high number of bankruptcy prediction models. They are generally based on financial symptoms [3, 4, 5, 6]. Over the last 35 years, academic researchers from all over the world have dedicated their time to the search for the best corporate failure prediction model that can classify companies according to their financial health or failure risk [7, 8, 9]. There have been several previous proposals that applied operational research techniques and pattern recognition methods to predict business failure [10, 11, 12]. Methods such as discriminant analysis, logit analysis, recursive partitioning algorithm, and several others have been used in the past for the prediction of business failure. Although

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evaluation of a bankruptcy risk [15, 17, 18] and market research [15, 19]. This paper is organized as follows: In Section 2, an overview of RST is provided. In section 3, research methodology and the data selection method used in this study are described. The research findings are discussed in section 4. The paper ends in section 5 with the conclusions.

Intuitively, a RS is a set or a subset of objects that cannot be expressed exactly by employing available knowledge. If this information or knowledge consists of a set of objects described by another set of attributes, one can consider a RS as a collection of objects that cannot be precisely characterized in terms of the values of the set of attributes [25]. Any RS has a lower and an upper approximation in terms of classes of indiscernible objects. Thus, a RS is a collection of objects that, in general, cannot be precisely characterized in terms of the values of the set of attributes, while its lower and upper approximations can. The lower approximation consists of all objects which certainly belong to the set and can be certainly classified as elements of that set, using the set of attributes in the table. The upper approximation contains objects which possibly belong to the set and can be possibly classified as elements of that set using the set of attributes in the table [25]. A fundamental problem in the RS approach is discovering dependencies between attributes in an information table, because it allows reducing the set of attributes removing those that are not essential to characterize knowledge [5]. This problem will be referred to as knowledge reduction, and the main concepts related to this question are the core and the reduct. The most important result in this approach is the generation of decision rules because they can be used to assign new objects to a decision class by matching the condition part of one of the decision rule to the description of the object. So rules can be used for decision support [25]. Since the core is the intersection of all reducts, it is included in every reduct, i.e., each element of the core belongs to some reduct. Thus, in a sense, the core is the most important subset of attributes, for none of its elements can be removed without affecting the classification power of attributes. Complexity of computing all reducts in an information system is rather high. However, in many applications, one does not need to compute all reducts, but only some of them, satisfying specific requirements, which is much simpler. There are many approaches to compute reducts [15]. The resulting confusion matrix from applying the generated rules on the discrete test set indicates how successfully the rules classified the objects in the test set. The measuring unit used is accuracy. Accuracy equals the number of objects correctly classified divided by the number of objects classified altogether. A number of algorithms are available both for discretization and reduct computation [26]. There are mainly three algorithms, genetic, Johnson’s, and Holte’s, in Rosetta software for reduct computation [27]. Johnson’s algorithm uses a simple greedy algorithm to compute single reducts only, however genetic algorithm is an implementation of a genetic algorithm for computing minimal hitting sets. In general, the genetic algorithm computes more reducts than the Johnson’s

2 An Overview of the Rough Set Theory Rough Set theory (ST), which proposed by Pawlak, has attracted the attention of many researchers and practitioners all over the world during the last decade. This has led to many scholarly contributions in its further development and applications [5, 19, 20, 21, 22]. For algorithmic reasons, information about objects is represented in the form of an information table. The rows of the table are labeled by objects, whereas columns are labeled by attributes (or criteria) and entries of the table are attribute values (evaluations). An information table where the set of attributes is split into condition and decision attributes is called decision table [23]. Each decision rule is characterized by the strength of its suggestion, that is, the number of objects satisfying the condition part of the rule and belonging to the suggested decision class. In the case of approximate rules, the strength is calculated for each possible decision class separately. Procedures for generating decision rules from a decision table operate on inductive learning principles [5]. The RS method accepts both quantitative and qualitative variables. It derives a number of decision rules (deterministic and non-deterministic sorting rules) or if… then rules. First, a range of minimal subsets of independent attributes is constructed. A subset of attributes is called a minimal subset if this subset has the same sorting quality as the whole set of attributes. Then, the core of attributes is defined as the intersection of all minimal subsets. Next, a reduced decision table is constructed, in which the redundant attributes are eliminated. Finally, on the basis of this decision table, the set of sorting rules, the sorting algorithm, is derived and firms are classified by matching their description to the set of sorting rules [7, 24]. The starting point of the RST is the indiscernibility relation, generated by information about objects of interest. The indiscernibility relation is intended to express the fact that, due to the lack of knowledge, we are unable to discern some objects employing the available information [15]. The indiscernibility relation may be formulated in quite general mathematical framework, but for the sake of intuition, it can be defined in reference to an information table called also an information system or an attributevalue table. Each subset of attributes determines a partition (classification) of all objects into classes having the same description in terms of these attributes [15].

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algorithm, thus Rosetta generates a larger number of rules when using the genetic algorithm compared with using the Johnson’s algorithm. More details about the Rosetta system and the different algorithms available can be found elsewhere [26, 27].

years ago). Table 1 is given for decision attributes, where “1” indicates a healthy bank and “0” indicates a failed bank. Table 1. Privately-owned Commercial Banks in Turkey from 1995 to 2001 Code Privately-owned Commercial Banks

3 The Methodology

a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 a13 a14 a15 a16 a17 a18 a19 a20 a21

Adabank A.S. Akbank T.A.S. Alternatif Bank A.S. Anadolubank A.S. Birlesik Turk Korfez Bankası A.S. Denizbank A.S. Fiba Bank A.S. Finans Bank A.S. Koçbank A.S. MNG Bank A.S. Oyak Bank A.S. Pamukbank T.A.S. Sekerbank T.A.S. Tekstil Bankası A.S. Turkish Bank A.S. Turk Dıs Ticaret Bankası A.S. Turk Ekonomi Bankası A.S. Turkiye Garanti Bankası A.S. Turkiye Imar Bankası T.A.S. Turkiye Is Bankası A.S. Yapı ve Kredi Bankası A.S. Banks Under the Department Insurance Fund a22 Turk Ticaret Bankası A.S. (Jan 6, 1997) a23 Bank Ekspres A.S. (Dec 12, 1998) a24 Interbank (Jan 7, 1999) Turkiye Tutunculer Bankası Yasarbank a25 A.S. (Dec 21,1999) a26 Egebank A.S. (Dec 21, 1999) Yurt Ticaret ve Kredi Bankası A.S. (Dec a27 21, 1999) a28 Sumerbank A.S. (Dec 21, 1999) a29 Eskisehir Bankası T.A.S. (Dec 21, 1999) a30 Demirbank T.A.S. (Dec 6, 2000) a31 Etibank A.S. (Oct 27, 2000) a32 Bank Kapital Türk A.S. (Oct 27, 2000) a33 Kibris Kredi Bankasi (Sep 27, 2000) a34 Bayindirbank A.S. (July 9,2001) Ege Giyim Sanayicileri Bankası A.S. (July a35 9, 2001) a36 Iktisat Bankasi T.A.S. (Mar 15, 2001) a37 Milli Aydın Bankası T.A.S. (July 9, 2001) a38 Sitebank A.S. (July 9, 2001) a39 Toprakbank A.S. (Nov 30, 2001) a40 Kentbank A.S. (July 9, 2001) a41 Ulusal Bank T.A.S. (Feb 28, 2001)

The main objective of this study was to investigate the reasons of bankruptcies in the Turkish banking system during 1995-2007 period using RST. The number of banks in Turkey in 1995 was 41. The first bank failure (Turk Ticaret Bankasi) took place in 1997. Further failures took place until 2003 when the total number remaining banks declined to 29. There have been no more bankruptcies during the 2004 – 2007 period. At the web site of the Banks Association of Turkey, ratios of all the banks in the Turkish banking sector are given in detail [28]. The files are presented in two sections; ratios between years of 1988-2000 and the ratios between years of 2001-2006. For 1988-2000, 49 ratios are defined and reported. After the economic crisis of 2001, these ratios were redefined and increased to 60. For the 2001-2006 period, the information on failed banks has been removed and only ratio information on banks in activity has been given. The commercial banks are examined under 5 groups in different numbers according to years (Table1). The basic reason to examine the banks under 5 groups is to study the bankrupted banks and non-bankrupted banks within same years and to consider that they are influenced from the economical events in the same ratio. For instance, 40 of 41 banks in Group I are healthy and one of them is bankrupted. Turk Ticaret Bank among these 41 banks bankrupted in 1997 (Jan. 6, 1997 bankruptcy) and other 40 banks continued their activities in 1997. When we examine the bankruptcy reasons of Turk Ticaret Bank from ratios, we also have to examine the other 40 banks in years having the same economical indicators. For this reason, 41 banks in Group I are examined together in years of 1997 (current year), 1996 (one year ago) and 1995 (two years ago). This collective examination is performed individually for 20 banks that went bankrupt (the assets of these banks were transferred to government-owned insurance fund) between1997-200. These banks are divided into 5 groups; 40 banks (39healthy, 1-failed) in Group II are examined in years of 1998 (current year), 1997 (one year ago) and 1996 (two years ago); 39 banks (33-healthy, 6-failed) in Group III, in years of 1999 (current year), 1998 (one year ago; ) and 1997 (two years ago); 33 banks (29-healthy, 4-failed) in Group IV, in years of 2000 (current year), 1999 (one year ago) and 1998 (two years ago) and 29 banks (21-healthy, 8-failed) in Group V, (data for 2001, current year, is not available), in year of 2000 (one year ago) and 1999 (two

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G-I G-II G-III G-IV G-V

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0 1 1

0 1

0

-

-

1

1

0

-

-

1

1

0

-

-

1

1

0

-

-

1 1 1 1 1 1 1

1 1 1 1 1 1 1

0 0 1 1 1 1 1

0 0 0 0 1

0

1

1

1

1

0

1 1 1 1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

0 0 0 0 0 0

1: Healthy, 0: Failed

Data on 49 variables are provided at the Banks Association of Turkey [28]. Only 36 of these variables were relevant for the purposes of this study and were selected (Table 2). These variables were chosen to create condition attributes of the information table used in the study.

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Table 2. Financial Ratios Investigated

the current year of the banks under the same economical conditions are determined. In this way, 14 different information tables are organized for examination. Genetic algorithms do not produce suitable solutions for us. If we make reduction and then filter with genetic algorithms, we will eliminate the characteristics of the bank or banks that bankrupted. Since the number of failed banks is less than the number of banks that continue their activities, reduction process will be problematic. For this reason, the Johnson’s algorithms produce better solutions in reduction process.

Liqu idity

Assets Quality

Capital Ratios (%)

Ratio Var Definitions cr1 Standard Capital Ratio (This was the ratio which was calculated by the banks according to the Decree no.23388 that was published by the Under secretariat of the Treasury.) cr2 (Shareholders' Equity +T. Income)/Total Assets cr3 (Shareholders' Equity + T. Income)/(Deposits + Non-deposit Funds) cr4 Net Working Capital/Total Assets cr5 (Shareholders' Equity+ Total Income)/(T. Assets + Contingencies and Commitments) cr6 Fx Position/Shareholders' Equity aq1 Total Loans/Total Assets aq2 Non Performing Loans/Total Loans aq3 Permanent Assets/Total Assets aq4 Fx Assets/Fx Liabilities li1 Liquid Assets/Total Assets li2 Liquid Assets /(Deposits + Non-deposit Funds) li3 Fx Liquid Assets/Fx Liabilities pr1 Net Income(Loss)/Average T. Assets pr2 Net Income(Loss)/Average T. Assets pr3 Net Income(Loss)/Average Share-in Capital pr4 Income Before Tax / Average Total Assets pr5 Provision for Loan Losses/Total Loans pr6 Provision for Loan Losses / Total Assets ie1 Net Interest Income After Provision/Average T. Assets ie2 Interest Income/Interest Expenses ie3 Non-Interest Income/Non-Interest Expenses ie4 Total Income/Total Expenditure ie5 Interest Income/Average Profitable Assets ie6 Interest Expenses/Average Non-Profitable Assets ie7 Interest Expenses/Average Profitable Assets ie8 Interest Income/Total Income ie9 Non-Interest Income/Total Income ie10 Interest Expenses/Total Expenses ie11 Non-Interest Expenses/Total Expenses ar1 (Salaries and Emp'ee Benefits +Reserve for Retirement)/T. Assets ar2 (Salary and Emp'ee Bene.+ Res. for Retire.)/No. of Pers. (Bil.TL) ar3 Reserve for Seniority Pay/No. of Personnel (Billion TL) ar4 Operational Expenses/Total Assets ar5 Provisions except Provisions for Income Tax/Total Income ar6 Provisions including Provisions for Income Tax/Total Income

4 Empirical Results

Activity Ratios (%)

Income-Expenditure Structure (%)

Profitability (%)

As was previously mentioned, many studies used statistical methods successfully to determine the bankruptcy reasons of banks and other types of companies. The RST has been used in many fields during the last 10 years in order to predict bankruptcies. The negative changes in ratios of banks or companies according to the economical conditions they experience may give danger signals for the future bankruptcy events, and they must be recognized correctly. Did the attributes that ensure discrimination between the banks or companies in the bankrupted year give the same signals 1 year ago or 2 years ago? In other words, were the ratio characteristics that ensure discrimination in a year when banks or companies went bankrupt same 1 year or 2 years ago? Table 3. Decision rules for Turk Ticaret Bank

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1 2 3 4 5 6 7 8

4 2 3

1 1 1 4 1 2 1 1 1 1 2 0

7 8 8 7 8 7 1

2 4 3

1 1 1 2 1 3 1 2 1 2 1 2 2 0

8 4 5 2 10 3 3 8 2 8 4 8 2 8 1 1 1

1 1 1 1 1 1 1 0

S

cr1 cr2 cr4 cr5 aq2 pr2 D

Year 1997 S

cr1 cr2 cr4 cr5 li2 pr6 D

Rule cr1 cr2 cr4 ie8 D

The first step of the analysis involves recoding the quantitative ratios (continuous variables) into qualitative terms (use of quartiles (-∞,0.25]-low, (0.25, 0.50]-medium, (0.50,0.75]-high and (0.75, ∞)-very high) with corresponding numeric values such as 1, 2, 3 and 4. The recoding has been done by dividing the original domain into subintervals. This recoding is not imposed by the RST, but it is very useful in order to draw general conclusions from the ratios in terms of dependencies, reducts and decision rules [5]. It was decided to recode the information tables using 4 subintervals based on the quartiles for the actual ratios (for the current year, a year ago, and two years ago) for the whole sample. The subintervals were assigned the highest code (code 4) for the best subinterval to develop a coded information table. In the second step, the recoded 36 condition attributes (Table 2) and decisions attributes belong to each group (Table 1) are examined individually for each year by using the ROSETTA GUI Version 1.4.41 software [27]. For each group, the condition attributes that effect the decision attributes for two years ago, one year ago, and

Year 1996 S

Year 1995

8 8 8 8 8 8 7 1

D: Decision, S: Strength

If one can recognize of danger signals 1 year or 2 years before the actual bankruptcy, perhaps necessary actions can be taken to avoid the failure. For example, when the ratios of the Turk Ticaret Bank that bankrupted on Jan 6, 1997 and ratios of other 40 banks are examined together for years 1995, 1996 and 1997, the low capital ratios of this bank give danger signals. In year 1995, cr1-low and ie8-medium and in 1996, li2-medium and pr6-medium indicate that the economical indicators are in low level. In 1997 when the bank bankrupted, cr5 and pr2 are in low level (Table 3). The decision rules on the Bank Express that bankrupted on Dec 12, 1998 are given in

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Table 6. Decision Rules for Group IV

Table 4. When the ratios of Bank Express and of 39 banks that were active in 1998 are examined together, it is seen that capital ratios are the attributes that ensure discrimination.

1 4 1 2 2 1 3 3 1 4 4 1 5 2 1 6 3 1 7 3 1 8 1 2 0 9 2 2 0 1 1 0 10

Table 4. Decision Rules for Bank Ekspres

4 2 3 1

1 1 1 1 1 4 1 3 1 2 0

8 8 8 8 8 8 7 1

11

In 2001, a big financial crisis was experienced in the Turkish economy and economical indicators were all down. One of the sectors greatly affected from that economical crisis was the finance sector. In 2001, many companies went bankrupt including 8 commercial banks. The economical crisis of 2001 was not the result of economical change of that year. It was the result of final explosion of the economical disorder that continued for years.

The year when the commercial banks in Turkey faced with economical crises for the first time and collective bankruptcies experienced is 1999. 6 banks bankrupted in 1999. When Table 5 is examined, it is seen that capital ratios and profitability ratios for total 39 banks (33-healthy, 6-failed) were low 2 years before (1997) and 1 year before (1998). Low capital ratios ensured discrimination between banks in great extent in 1999.

Table 7. Decision rules for Group V Year 1999

Table 5. Decision rules for Group III Year 1998

Year 1999

Rule cr1 cr2 cr4 cr6 aq1 aq3 li3 pr5 pr6 D S cr1 cr2 cr4 aq1 aq3 li1 li2 pr3 ar3 D S cr1 cr2 cr3 cr4 cr6 aq1 pr3 D S

Year 1997

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

4 3

18 4 19 4 18 19 3 19 3 19 4 3 19 1 10 2 19 3 3 3 1 10 1 10 1 10 3 2 1 10 19 2 1 10 4 3 1 10 4 19 1 10 3 4 3 19 19 19 3 3 1 1 1 19 03 06 316 2 101 2 101 1 1 11 1 1 1 1 03 06 1 1 1 1 01 04 1 2 03 1 203 1 3 01 2 2 01

1 2 3 4 5 6 7 8 9 10 11 12 13 14

3 4 3 3

4 2

2 2 2 1 1 1 2

2 2 1

1 1 1 3 1 1 3 1 1 3 0 2 0 3 0 3 0 0 0 0

7 7 7 7 2 8 7 1 3 2 1 2 1 1

4 3

7 7 7 8 7 7 1 7

1 1 3 1 3 1 3 1 4 1 2 1 0 1 0

When ratios of 29 banks (21-healthy, 8-failed) are examined for 1999 and 2000 years, it is seen that assets quality, profitability, income-expenditure structure and activity ratios were effective in addition to capital ratios (as ratios of bankrupted banks were removed from the list, ratios information of 2001 year could not be obtained). Table 7 indicates that many ratios in the banking sector began to change in a negative manner in years of 1999 and 2000 indicating that danger was about to appear. After the crisis, as indicated before, there were major measures taken in the banking sector including the creation and reporting of additional ratios (ratios increasing from 49 to 60) to predict potential failures in advance. As a result, from 2001 until today, only 2 banks bankrupted and other banks have continued their activities.

After 1999, bankruptcies of commercial banks in the Turkish banking system continued and in 2000, 4 banks bankrupted. When Table 6 is examined, it is seen that capital ratios ensured discrimination between the banks that bankrupted and the banks that continued their activities and additionally, assets quality ratios were also the attributes that caused discrimination. While in 1998 the attributes causing the discrimination were low and medium, in 1999, they improved slightly as medium and high but in 2000, they again decreased to low and medium levels.

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Year 2000 S

2 3

7 8 8 8 7 7 7 1 1 2

S

8 9 7 8 8 1

1 1 1 1 1 1 1 0 0 0

cr1 cr2 cr4 cr6 aq4 pr1 pr2 D

1 1 1 3 1 4 1 1 2 0

Year 2000

2 7 1 7 4 4 8 1 7 3 3 7 1 8 2 2 8 3 1 8 4 9 2 1 8 3 2 8 1 7 4 3 7 1 7 2 3 1 2 1 7 3 2 0 1 2 1 1 1 2 2 1 1 0 1 3 2 0 2

Rule cr1 cr2 cr3 cr4 cr6 aq2 aq3 pr1 pr3 ie7 ar6 D

4 3 2

S

6 7 8 8 7 8 8 8 1

cr1 cr3 cr4 cr5 cr6 D

1 1 1 1 1 1 1 1 2 0

Year 1998 S

S

1 2 2 4 3 3 4 3 5 4 6 2 7 3 8 3 9 1

cr1 cr2 cr4 pr5 D

aq3 D

Year 1997

Rule cr1 cr2 cr4 cr5

Year 1996

Year 1999

Rule cr1 cr2 cr4 cr6 aq2 aq3 aq4 D S cr1 cr2 cr3 cr4 cr6 aq2 ar4 ar5 D S cr1 cr4 cr5 cr6 aq1 aq3 pr1 pr2 D S

Year 1998

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[13] Pawlak, Z., Rough Sets, International Journal of Information and Computer Sciences, 11, 1982, 341-356 [14] Greco S.; Matarazzo B,; Slowinski R., Rough Sets Theory for Multicriteria Decision Analysis, European Journal of Operational Research, 129, 2001, 1-47 [15] Pawlak Z., Rough Set Approach to Knowledge-Based Decision Support, European Journal of Operational Research 99, 1997, 48-57 [16] Krysifiski, J., Application of the Rough Sets Theory to the Analysis of Structure-Activity-Relationships of Antimicrobial Pyridinium Compounds, Die Pharmazie 50, 1995, 593-597 [17] Stowifiski, R.; Zopounidis, C., Working Paper: Applications of the Rough Set Approach to Evaluation of Bankruptcy Risk, Decision Support System Laboratory, Technical University of Crete, Chania, 93-08, 1993 [18] Stowifiski, R.; Zopounidis, C., Rough Set Sorting of Firms According to Bankruptcy Risk, in: M. Paruccini (ed.), Applying Multiple Criteria Aid for Decision to Environmental Management, Kluwer, Dordrecht, Netherlands, 1994, 339-357 [19] Ziarko, W.; Katzberg, J., Control Algorithms Acquisition, Analysis and Reduction: Machine Learning Approach, Knowledge-Based Systems Diagnosis, Supervision and Control, Plenum Press, Oxford, 1989, 167-178 [20] Pawlak, Z., Rough Sets; Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, Dordrecht, 1991 [21] Slowinski R., Rough Set Approach to Decision Analysis. AI Expert Magazine 10 (3), 1995, 18-25 [22] Pawlak, Z.; Slowinski, R., Rough Set Approach to Multiattribute Decision Analysis, European Journal of Operational Research, 72, 1994, 443-459 [23] Greco S.; Matarazzo B,; Slowinski R., Rough Approximation of a Preference Relation by Dominance Relations, European Journal of Operational Research, 117, 1999, 63-83 [24] Slowinski, R.; Zopounidis, C., Application of the Rough Set Approach to Evaluation of Bankruptcy Risk, International Journal of Intelligent Systems in Accounting, Finance and Management, 4, 1995, 27-41 [25] Díaz Z.; Segovia M.J.; Fernández J.; Pozo E.M., Machine Learning and Statistical Techniques: An Application to the Prediction of Insolvency in Spanish Non-life Insurance Companies, The International Journal of Digital Accounting Reseach [26] Hvidsten T. R.; Bjanger M. S.; Komorowski J., Fault Dıagnosıs in Rotating Machinery Using Rough Sets and Rosetta: Extended Abstract [27] Øhrn A., Rosetta, Technical Reference Manual, 1999, http://www.idi.ntnu.no/_aleks/rosetta [28] Banks Association of Turkey, http://www.tbb.org.tr/ english/bulten/yillik/2000/ratios.xls

5 Conclusions This study examined the bankruptcy reasons of the Turkish commercial banks between years of 1995-2007 by using the RST and tried to find the attributes that caused discrimination. In general, low capital ratios indicated a danger for the bank bankruptcies. In addition, low and medium assets quality and profitability ratios were the leading indicators in predicting future bankruptcies. The Turkish banking system was used as a case analysis in this study to determine whether RST can be applied in discriminating between failing banks and successful banks. The result was that, this technique provides strong results in explaining bank bankruptcies in Turkey. References: [1] Ahna, B.S.; Chob S.S.; Kimc C.Y., The Integrated Methodology of Rough Set Theory and Artificial Neural Network for Business Failure Prediction, Expert Systems with Applications, 18, 2000, 65–74 [2] Mckee T.E., Research Article: Developing a Bankruptcy Prediction Model via Rough Sets Theory, International Journal of Intelligent Systems in Accounting, Finance & Management, 9 (3), 159 – 173. [3] Ooghe H.; Prijcker S. D., Working Paper: Failure Proceses and Causes of Company Bankruptcy: A Typology, Steunpunt OOI: May 2006 [4] Beynon M.J.; Peel M.J., Variable Precision Through Rough Set theory and Date Discretisation: An Application to Corporate Failure Prediction, Omega: International Journal of Management Science 29 (6), 2001, 561–576 [5] Dimitras A.I.; Slowinski R.; Susmage R.; Zopounidis C., Business Failure Prediction Using Rough Sets, European Journal of Operational Research, 144 (2), 1999, 263–280 [6] Ooghe H.; Joos P.; De Bourdeaudhuij C., Financial Distress Models in Belgium: The Results of a Decade of Empirical Research, The International Journal of Accounting, 30 (3), 1994, 245–274 [7] Balcaen S.; Ooghe H., Alternative Methodologies in Studies on Business Failure: Do They Produce Better Results than the Classic Statistical Methods?, Vlerick Leuven Gent Management School Working Paper Series 16, 2004 [8]Altman, E.I., The Success of Business Failure Prediction Models: An International Survey, Journal of Banking and Finance 8 (2), 1984, 171-198 [9] Dimitras, A.I.; Zanakis, S.H.; Zopounidis, C., A Survey of Business Failures with an Emphasis on Prediction Methods and Industrial Applications, European Journal of Operational Research, 90, 1996, 487-513. [10] Ambrose J. M.; Carol, A.M., Using Best Ratings in Life Insurer Insolvency Prediction, Journal of Risk and Insurance, 61, 1994, 317-327 [11] Barniv, R., Accounting Procedures, Market Data, Cashflow Ffigures and Insolvency Classification: The Case of the Insurance Industry, The Accounting Review, 65(3), 1990, 578-604 [12] Tam, K.Y., Neural Network Models and the Prediction of Bankruptcy, Omega, 19(5), 1991, 429-445

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