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Invited Review

Bankruptcy prediction in banks and firms via statisticaland intelligent techniques A review

P. Ravi Kumar, V. Ravi *

Institute for Development and Research in Banking Technology, Castle Hills Road # 1, Masab Tank, Hyderabad 500 057 (AP), India

Received 19 July 2005; accepted 11 August 2006Available online 17 November 2006

Abstract

This paper presents a comprehensive review of the work done, during the 19682005, in the application of statistical andintelligent techniques to solve the bankruptcy prediction problem faced by banks and firms. The review is categorized bytaking the type of technique applied to solve this problem as an important dimension. Accordingly, the papers are groupedin the following families of techniques: (i) statistical techniques, (ii) neural networks, (iii) case-based reasoning, (iv) decisiontrees, (iv) operational research, (v) evolutionary approaches, (vi) rough set based techniques, (vii) other techniques subsum-ing fuzzy logic, support vector machine and isotonic separation and (viii) soft computing subsuming seamless hybridiza-tion of all the above-mentioned techniques. Of particular significance is that in each paper, the review highlights the sourceof data sets, financial ratios used, country of origin, time line of study and the comparative performance of techniques in

terms of prediction accuracy wherever available. The review also lists some important directions for future research. 2006 Elsevier B.V. All rights reserved.

Keywords: Bankruptcy prediction; Banks; Firms; Statistics; Neural networks; Fuzzy logic; Case-based reasoning; Decision trees; Evol-utionary approaches; Operations research; Rough sets; Support vector machine and soft computing; Intelligent techniques

1. Introduction

The prediction of bankruptcy for financial firmsespecially banks has been extensively researched

area since late 1960s[3]. Creditors, auditors, stock-holders and senior management are all interested inbankruptcy prediction because it affects all of themalike[121]. The health of a bank or firm in a highlycompetitive business environment is dependent

upon (i) how financially solvent it is at the inception,(ii) its ability, relative flexibility and efficiency in cre-ating cash from its continuous operations, (iii) itsaccess to capital markets and (iv) its financial capac-

ity and staying power when faced with unplannedcash short-falls. As a bank or firm becomes moreand more insolvent, it gradually enters a dangerzone. Then, changes to its operations and capitalstructure must be made in order to keep it solvent(http://www.solvency.com/solvency.htm).

The most precise way of monitoring banks is byconducting on-site examinations. These examina-tions are conducted on a banks premises by regu-lators every 1218 months, as mandated by the

0377-2217/$ - see front matter 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.ejor.2006.08.043

* Corresponding author. Tel.: +91 40 23534981; fax: +91 4023535157.

E-mail addresses: [email protected],[email protected](V. Ravi).

European Journal of Operational Research 180 (2007) 128

www.elsevier.com/locate/ejor
http://www.solvency.com/solvency.htmmailto:[email protected]:[email protected]:[email protected]:[email protected]://www.solvency.com/solvency.htm

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Federal Deposit Insurance Corporation Improve-ment Act of 1991. Regulators utilize a six part rat-ing system to indicate the safety and soundness ofthe institution. This rating, referred to as the CAM-ELS rating, evaluates banks according to their basic

functional areas: capital adequacy

, asset quality

,management expertise, earnings strength, liquidityand sensitivity to market risk. While CAMELS rat-ings clearly provide regulators with important infor-mation, Cole and Gunther [20]reported that theseCAMELS ratings decay rapidly. Fraser [30] notedthat banks perform better by holding relativelymore securities and fewer loans in their portfolios.Gady[32]and Fraser[30]showed that core depositfunding is beneficial for banks, particularly demanddeposits, which are non-interest bearing. Gady [32]has indicated that high-performance banks are able

to generate more interest or non-interest incomethan under performing banks. Wall [117] observedthat higher profit banks rely more on equity fund-ing. Brewer et al. [15] observed that firms usedthe derivative instruments to change their risk expo-sure. They also concluded that there was a negativecorrelation between risk and derivatives usage.Haslem et al. [44] determined the impact of typesof strategies followed by individual banks relatedto the relative profitability performance. Kwastand Rose [60] employed statistical cost accounting

techniques to examine the relationship betweenbank profitability and pricing and operatingefficiency.

This paper presents a comprehensive survey of anumber of research works published during 19682005, where various statistical and intelligent tech-niques were applied to solve bankruptcy predictionproblem in banks and firms. The usefulness of thecurrent review paper is that the papers are catego-rized, primarily, according to the techniqueemployed therein. This aspect paves the way forthe researchers from the statistical and the artificialintelligence/soft computing community to shiftfocus on this exciting problem of bankruptcy pre-diction by applying their newest and novel ideas.This will only enhance and enrich the bankruptcyprediction research further as these researchers arelikely to come out with robust and high performingmodels. The review paper is aimed at attractingfresh graduates, researchers and academics fromfinance, banking, statistics and artificial intelli-gence/soft computing, since bankruptcy predictionis a multi-disciplinary area. The current review is

different from the earlier reviews, presented in Sec-

tion3, in the following aspects: (i) It is categorizedwith respect to the techniques employed. (ii) It isby far, the most comprehensive and organized withrespect to various dimensions of review such as thefinancial ratios used, source of data set, country of

origin, time line of study, type of industry viz., bankor firm as detailed in Tables 2 and 3. (iii) It alsogives the reader a brief overview of the techniquesemployed. (iv) It gives the reader an unbiased com-parison of the statistical and intelligent techniques.(v) It can be considered as a starting point to pursueresearch in bankruptcy prediction.

1.1. Earlier reviews

This section presents an overview of the reviewpapers published earlier on bankruptcy prediction.

Scott[99]reviewed several empirical and theoreticalmodels and found a substantial amount of overlapbetween these two lines of research. He concludedthat the success of empirical models suggested theexistence of a strong underlying regularity, thoughthey are not based on explicit theory. Dimitraset al.[25]presented a review of the articles publishedduring 19321994 in various journals specialized inaccounting, finance, operation research and decisionscience. They selected 47 articles restricted to (i)

journal articles that presented models and (ii) indus-

trial and retail applications. Their framework ofstudy was based on the country, year of publication,industry type, sample periods and method. Theyreviewed a total of 59 models and variables usedin these articles. OLeary [84] proposed a metaanalysis of the use of neural networks to predictcorporate failure. His review was across dimensionssuch as the software used, the input variables, thenature of the hidden layer used, number hiddennodes and statistical analysis of results. Tay andShen [110] reviewed the application of variousrough set based models to bankruptcy predictionand concluded that rough set models were promis-ing alternative to conventional methods. Daubieand Meskens [23] reviewed the prediction modelsapplied to business failure in banks and firms. Theydiscussed the causes, symptoms, process and reme-dies of failure. They reviewed papers published dur-ing 19682000 in journals specialized in accounting,finance, operations research and decision science.Calderon and Cheh [17] reviewed the applicationsof neural networks in bankruptcy prediction. Forevery study they presented the number of input vari-

ables, learning sample size, testing sample size and

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software used. They explained the comparative effi-ciency of different techniques.

The rest of the paper is organized as follows:Section 2 presents an overview of the intelligenttechniques. Section 3 reviews papers dealing with

statistical techniques while Section 4 presents theworks employing various NN architectures. Section5 presents CBR applications while Section 6describes decision tree applications to the problem.Section 7 reviews the applications of evolutionaryapproaches and Section 8 presents applications ofoperational research to the problem. Section9pre-sents the papers employing rough sets and Section10 describes the application of other techniquessubsuming fuzzy logic, support vector machineand isotonic separation to the problem. Finally,Section11presents the soft computing applications.

Section12presents some of the important insightsthat emerged out of the survey. Section 13 suggestssome future research directions in the field and con-cludes the review.

2. Review methodology

As mentioned earlier, the review is conducted intwo broad categories: (i) statistical and (ii) intelli-gent techniques. Among statistical techniques, themethods covered are: linear discriminant analysis

(LDA), multivariate discriminate analysis (MDA),quadratic discriminant analysis (QDA), logisticregression (logit) and factor analysis (FA). Theintelligent techniques covered in the study belongto (i) different neural network (NN) architecturesincluding multi-layer perception (MLP), probabilis-tic neural networks (PNN), auto-associative neuralnetwork (AANN), self-organizing map (SOM),learning vector quantization (LVQ) and cascadecorrelation neural network (Cascor), (ii) decisiontrees, (iii) case-based reasoning, (iv) evolutionaryapproaches, (v) rough sets, (vi) soft computing(hybrid intelligent systems), (vii) operationalresearch techniques including linear programming(LP), data envelopment analysis (DEA) and qua-dratic programming (QP), (viii) other intelligenttechniques including support vector machine, fuzzylogic techniques. Under each category, the papersare reviewed in the chronological order. Thus themost important dimension of the present review isthe type of techniques applied. The review is con-ducted across other dimensions also such as (i)study pertaining to bank or firm (type of firm if

mentioned), (ii) source of data, (iii) various financial

ratios used as explanatory variables, (iv) the yearsduring which data was collected, (v) number ofyears prior to which prediction was made (if avail-able) and (vi) results obtained (when available inconcise form) in each study. Further, the review

concentrated on the papers published in peer-reviewed journals/international conferences/editedvolumes in the areas of accounts, finance, manage-ment, operational research, neural networks, expertsystems and decision support systems. All theunpublished works in terms of Ph.D. thesis, work-ing papers and internal reports are excluded fromthe scope of the review. Moreover, in a paper, whenmultiple techniques are compared in their stand-alone mode, the technique proposed in that paperis taken as the main criterion and accordingly thepaper is categorized in that family. For example,

when in a paper, NN, DA and logit (logistic regres-sion) are compared in their stand-alone mode andNN is proposed in that paper, then the paper isreviewed under the NN section.

The present review indicates that neural networksfamily with 25 papers is the most widely appliedtechnique. The soft computing family with 15 papersand statistical family with 11 papers follow this.Then, rough sets were applied in six papers and othertechniques accounted for five papers, while CBR andOR techniques had four papers each. Also, evolu-

tionary approaches and decision trees figured inthree and two papers, respectively. Further, five ear-lier review papers are also included in the currentreview. Table 1 presents the main idea behind theintelligent techniques, their advantages and disad-vantages. Table 2 lists the financial ratios used ineach of the papers.Table 3presents for all papers,the details such as the entity for which the studywas done banks or firms; source of data; countryof origin; sample size; techniques used in the studyand the time line of the study and the number ofyears prior to prediction, wherever available.

2.1. Overview of intelligent techniques

2.1.1. Fuzzy set theory

Fuzzy set theory, proposed by Zadeh [124], hasfound a number of applications. It is a theory ofgraded concepts. It provides a mathematical frame-work where vague, conceptual phenomena can berigorously studied[127]. Fuzzy logic models humanexperiential knowledge in any domain. Whenapplied to solve process control or prediction prob-

lems fuzzy logic takes the help of the knowledge of

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the domain expert and employs fuzzy mathematicsto come out with fuzzy inference systems. Fuzzylogic can also be used to derive fuzzy ifthen rulesfrom data to solve classification problems.

2.1.2. Neural networks

Neural networks [62,72] offer a computationalparadigm inspired by biological neural networks

of human nervous system. A neural network is a

system of massively parallel, interconnected com-puting units called neurons, arranged in layers.The neural networks found extensive applicationsin financial services. The multi-layer perceptron(MLP)[95], radial basis function network (RBFN)[81], probabilistic neural network (PNN)[104], cas-cade correlation neural network (Cascor) [28],learning vector quantization (LVQ) [35,56], self-

organizing feature map (SOM) [56] are some of

Table 1Merits and demerits of intelligent techniques

Technology Basic idea Advantages Disadvantages

1 FL Models imprecision and ambiguityin the data using fuzzy sets andincorporates the human

experiential knowledge into themodel

Good at deriving humancomprehensible fuzzy ifthen rules;It has low computational

requirements

Arbitrary choice of Membershipfunction skews the results, althoughtriangular shape is the most often

used one. Secondly, the plethora ofchoices for membership functionshapes, connectives for fuzzy setsand defuzzification operators are thedisadvantages

2 NN Learn from examples using severalconstructs and algorithms just likea human being learns new things

Good at function approximation,forecasting, classification, clusteringand optimization tasks dependingon the neural network architecture

The determination of various para-meters associated with trainingalgorithms is not straightforward.Many neural network architecturesneed a lot of training data andtraining cycles (iterations)

3 GA Mimics Darwinian principles of evolution to solve highly nonlinear,

non-convex global optimizationproblems

Good at finding global optimum of ahighly nonlinear, non-convex

function without getting trapped inlocal minima

Does take long time to converge;May not yield global optimal

solution always unless it is aug-mented by a suitable direct searchmethod

4 CBR Learns from examples using theeuclidean distance and k-nearestneighbor method

Good for small data sets and whenthe data appears as cases; similar tothe human like decision-making

Cannot be applied to large data sets;poor in generalization

5 Rough sets They use lower and upperapproximation of a concept tomodel uncertainty in the data

They yield ifthen rules involvingordinal values to performclassification tasks

It can be (a) sometimes impracticalto apply as it may lead to an emptyset (b) sensitive to changes in dataand (c) inaccurate

6 SVM It uses statistical learning theory toperform classification andregression tasks

It yields global optimal solution asthe problem gets converted to aquadratic programming problem; Itcan work well with few samples

Selection of kernel and itsparameters is a tricky issue. It isabysmally slow in test phase. It hashigh algorithmic complexity and

requires extensive memory7 Decision

treesThey use recursive partitioningtechnique and measures likeentropy to induce decision trees ona data set

Many of them can solve onlyclassification problems while CARTsolves both classification andregression problems. They yieldhuman comprehensible binary ifthen rules

Over fitting can be a problem. Likeneural networks, they too require alot of data samples in order to getreliable predictions

8 DEA It uses linear programming to rankvarious alternatives/business unitsaccording to some input and outvariables

It has found numerous applicationsand gives exact solution

It yields only relative scoring of thebusiness units and not absoluteratings

9 SC Hybridizes fuzzy logic, neuralnetworks, genetic algorithms, etc.in several forms to derive the

advantages of all of them

It amplifies the advantages of theintelligent techniques whilesimultaneously nullifying their

disadvantages

Apparently, it has no disadvantages.However, it does require goodamount of data, which is not exactly

a disadvantage nowadays


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Table 2Financial ratios (variables) in each paper

Ref # Variables

[1] Cash flow/total liabilities, current assets/current liabilities (current ratio), inventories turnover, net income/total sales, netincome/total assets, net working capital/total assets, owners equity/total assets, (total borrowings + bonds payable)/totalassets

[2] Net income/total assets (return on assets (ROA)), net loan losses/adjusted assets, net loan losses/total loan, (net loanlosses + provision for loan losses)/income, non-performing loans/total assets

[5] Common equity/total capital (capitalization), cumulative profitability, debt services, stability of earnings, roa, liquidity, size[6] Debt cost, debt quality, growth, indebtedness, share of labour costs, short-term liquidity, size, turnover of assets[7] Book value/total assets, cash flow/total assets, gross operating income/total assets, ROA, price/cash flow, rate of change of

cash flow per share (ROC), rate of change of stock price, stock price volatility[8] Cash/current liabilities, cash/net sales, cash/total assets, cash flow/current liabilities, cash flow/total assets, cash flow/total debt,

current ratio, current assets/net sales, current assets/total assets, current liabilities/equity, earnings before interest and taxes(EBIT)/total interest payments, equity/fixed assets, equity/net sales, inventory/net sales, long-term debt/equity, market value ofequity/book value of debt, net income/total assets, net quick assets/inventory, net sales/total assets, operating income/totalassets, quick assets/current liabilities, quick assets/net sales, quick assets/total assets, rate of return/common stock holders,retained earnings/total assets, return on stock, total debt/equity, total debt/total assets, working capital/equity, workingcapital/net sales, working capital/total assets

[9] EBIT/total assets, market capitalization/total debt, retained earnings/total assets, sales/total assets, working capital/total assets[11] Complexity of capital structure, degree of competitiveness, firm age, fraud, intangible assets/net sales, natural log of total assetsdeflated the gross domestic product, ROA, ownership concentration, past losses, resignation, secured interest bearing debt/total liabilities, total interest bearing debt/total liabilities

[12] Agricultural loans/total assets, commercial real estate loans/total assets, construction loans/total assets, income before extraitems, large time deposits/total assets, insiders loans over net loans, natural log(total assets), net charge offs/total loans, ROA,net interest income/total assets, net loans/total assets, non-interest income/total assets, non-performing loans/primary capital,non-performing loans/total assets, past due loans/gross loans, primary capital/adjusted assets, provision for loan losses/totalassets, restructured loans/gross loans, return on equity, security gains (losses) and extra items/total assets, short-term assets lesslarge liabilities/total assets, total capital/total loans, total equity capital, total overhead expenses/total assets, undivided profitand capital reserve to total assets, yield on total assets

[13] Cash flow/total debt, current ratio, current liabilities/total debts, gross profit/sales, net income/stockholders equity, roa, sales/total assets

[16] Cash/current liabilities, cash/total assets, cost of goods sold/inventory, current ratio, current assets/total assets, current assets/

total sales, current liabilities/total assets, EBIT/total assets, inventory/sales, net income/net worth, net income/sales, ROA,quick assets/sales, quick assets/total assets, retained earnings/inventory, retained earnings/total assets, sales/cash, sales/networth, sales/total assets, total assets/gross national product (GNP) price-level, total liabilities/net worth, total liabilities/totalassets, working capital/sales

[18] Quick ratio, income ratio, interest expenses/average non-profitable assets, interest expenses/average profitable assets, interestexpenses/total expenses, interest income/interest expenses, liquid assets/(deposits + non-deposit funds), liquid assets/totalassets, net working capital/total assets, (salary and employee benefits + reserves for retirement)/no of personnel, (shareholdersequity + total income)/(depreciation + non-depreciation funds), (shareholders equity + total income)/total assets,(shareholders equity + total income)/(total assets + contingencies and commodities), standard capital ratio

[19] Cash/restricted current assets, equity ratio(equity/total assets), expired taxes, retained earnings/total assets, inventories, grossreturn, coverage of debt, net return, current ratio, quick ratio, debt ratio

[24] Abnormal increase in inventory and receivables, quick ratio, current ratio, debt/equity, dividend, funds flow ratio, ROA, networth, sales/total assets, total assets, trend in net income, working capital/total assets

[26] Current ratio, current liabilities/total assets, gross profit/total assets, inventories/working capital, (long-term debt + current

liabilities)/total assets, net income/gross profit, ROA, net worth/(net worth + long-term debt), quick assets/current liabilities,working capital/net worth

[29] Quick ratio, current ratio, income ratio (income/working capital)[31] Cash flow/total debt, current ratio, current assets/total assets, EBIT/total assets, log(interest coverage + 15), log (total assets),

market value of equity/total capitalization, ROA, quick assets/current liabilities, quick assets/total assets[36] Working capital/total assets, retained earnings/total assets, EBIT/total assets, market value of equity/total assets, sales/total

assets[37] EBIT/total assets, net income/net worth, total liabilities/total assets, total liabilities/cash flow, interest expenses/sales, general

and administrative expensive/sales, managers work experience, firms market niche position, technical structure facilities,organization-personnel, competitive advantage of firms, market flexibility

[44] Domestic cash, domestic investment securities, foreign cash, foreign investment securities, net domestic loans, net foreign loans,net income, total assets, total domestic interest bearing deposits, total domestic non-interest-bearing deposits, total equitycapital, total foreign interest bearing deposits, total foreign non-interest bearing deposits

(continued on next page)


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Table 2 (continued)

Ref # Variables

[45] EBIT/total assets, market value of equity/total debt, retained earnings/total assets, sales/total assets, working capital/totalassets

[51] Net operating cash flow to total assets, cash resources to total assets, cash flow cover (net operating cash flow to annual interestpayments), sales revenue to total assets, total debt to total equity, total debt to gross operating cash flow, working capital to

total assets (wc = current assets current liabilities)[53] Gross profit margin ((net sales-cost of goods sold)/net sales), market value of common stock, natural logarithms of tangible

asset turnover, (net income + depreciation)/number of shares, (cash flow per share), net income/total of common equity(earnings per share), sales/cash, sales/inventories, sales/receivables, total debt/total assets, total debt/total capital, workingcapital/total assets

[55] Equity ratio (equity/total assets), net income before depreciation and extraordinary items, net income before depreciation andextraordinary items of the previous year, operating margin

[57] Allowance for loan losses/total assets, bank holding companies total assets, bank total assets/bank holding co. (bhc) totalassets, certificate of deposit/total deposits, maximum change in assets/mean assets, maximum change in assets/mean changeassets, maximum change in loans past due at least 90 days/mean of numerator, net income after taxes/total assets, net interestincome/total assets, net loan charge-offs/total assets, non-deposit liabilities/total liabilities, provision for loan losses/totalassets, sum of key asset accounts/total assets, total assets, total equity/total assets, total loans and leases/total assets, totalsecurities/total assets

[62] EBIT/total assets, market value of equity/book value of debt, retained earnings/total assets, sales/total assets, working capital/total assets[64] Capital expenditure, common shares traded, consumer price index, current account balance/gross domestic product, current

assets/common shareholders equity, depreciation expenses, dividend/share, earnings/share, effective exchange rate, federalbudget/gross domestic product, government spending/gross domestic product, (long-term debt + short-term debt)/totalassets, market capitalization, money supply, net income/net sales, net sales/total assets, pre-tax income/net sales, purchaseprice of crude oil, relative strength index, research expenses, short-term interest rate, spread between short-term and long-terminterest rate, tax deferral and investment credit, total sources of fund/ total uses of fund, trade balance/gross domesticproduct

[65] Quick ratio, cash flow/sales, cash flow/stock holders equity, cash flow/total assets, cash flow/total borrowings and bond,change in payable/receivables, change in inventory/current assets, change in inventories turnover, change in payables/current liabilities, current ratio, current ratio trend, debtos ratio (days) (debtors * 365 days/sales), dividend/capital stock,financial expenses/sales, fixed assets/(stockholders equity + long-term liabilities), fixed assets turnover, fixed assetcomposition, fixed liability ratio, fixed ratio, gross profit/sales, growth rate of fixed asset, growth rate of net income, growth

rate of ordinary income, growth rate of sales, growth rate of total liabilities, growth rate of total assets, interest coverageratio, interest ratio, inventory/current assets, inventories turnover, net income/capital stock, net income/sales, net income/stockholders equity, net income/total assets, net working capital/total assets, net working capital turnover, operatingincome/sales, ordinary income/business capital, ordinary income/sales, ordinary income/stockholders equity, ordinaryincome/total assets, payable/current liabilities, payables/inventories, payables/receivables, stock holders equity/total assets,stock holders equity turnover, total assets turnover, (total borrowings + bonds payable)/total assets, total liabilitycomposition

[66] EBIT/total assets, market capitalization/total debt, retained earnings/total assets, sales/total assets, working capital/totalassets

[67] Average market equity/total capital, auditor, auditor opinion, bond rating, book equity/total capital, quick ratio, cash flow/fixed charges, cash flow/share, cash flow/total debt, cash flow margin, capital expenditure/share, capital lease, cost of goodssold/sales, current ratio, current liabilities/total liabilities, dividend, earnings/5 years maturity, earnings/total debt, earningsbefore interest and taxes (EBIT) drop, EBIT/sales, EBIT/share, EBIT/total assets, EBIT/total tangible assets, fixed chargecoverage, interest coverage, inventory turnover, log (interest coverage), log (total assets), long-term debt/equity, margin drop,

market equity/total capital, market value/total liabilities, net available for capital/total capital, net available for total capital/sales, ROA, net income/total debt, net profit margin, number of employees, operating income/sales, price/earning ratio, quickassets/sales, receivables turnover, retained earnings/total assets, retained earnings/tangible assets, sales/cash, sales/gross fixedassets, sales/receivables, sales/total assets, sales/total capital, sales/total tangible assets, standard deviation (EBIT/total assets),standard deviation (log (EBIT/total assets)), total debt/total assets, total debt/total capital, total investment, working capital/long-term debt, working capital/total assets, worth/total debt

[69] Average salary/employee, borrowing ratio, quick ratio, cash ratio(cash and market securities/total liabilities), cash earnings/share, cash flow margin, capital employed/employee, capital gearing, coverage debt, creditors ratio (days)(creditor*365 days/cost of sales), creditors turnover, current ratio, debtos ratio (days)(debtors*365 days/sales), debtos turnover, earnings margin,financial debt ratio, gross return, income gearing, inventories, net profit margin, net return, operating profit margin, operatingprofit/employee, pre-tax profit margin, preferences and loan/equity and reserves, quick assets/total assets, return on capitalemployed, return on long-term capital, return on net fixed assets, return on shareholders capital, return on shareholdersequity, sales/employee, stock ratio (days), stock turnover, tax ratio, trading profit margin, turnover/assets employed, turnover/

fixed assets, turnover/net current assets, working capital/total assets


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Table 2 (continued)

Ref # Variables

[70] Auditor opinion, audit qualification, cash/total assets, cash/current liabilities, commercial paper rating, current ratio, currentassets/net sales, current assets/total assets, debt rating, funds flow/total liabilities, net income/total assets, net worth, number ofyears of financial statements in database, number of consecutive years negative net income, number of consecutive years salesdecline, quick assets/current liabilities, sales, sales/total assets, sales/working capital, standard deviation of common stock rate

of return, stock exchange, total liabilities/net worth, total liabilities/total assets, working capital/total assets, yearly dividend[71] Charge-offs/(net operating income + loss provision), commercial and industrial loans/total loans, dividends/net income, equity

capital/adjusted risk assets, gross capital/adjusted risk assets, gross capital/risk assets, gross charge-offs/(net operatingincome + loss provision), liquid assets/total sources of funds, loans/total assets, loans and leases/total sources of funds, lossprovision/(loans + securities), roa, net income/total assets, net interest margin/earning assets, net interest margin (taxableequivalent)/earning assets, net liquid assets/total assets, non-interest expenses/operating revenue, operating expenses/operatingrevenues, total assets, total operating expenses/operating revenue

[73] Accounts receivables/sales, cash/total assets, current ratio, current assets/total assets, current assets/sales, inventory/cost ofgoods sold, long-term debt/total assets, ROA

[74] Cash/current liabilities, investment cash flow/net income, firm size, ROA[75] Cash/current liabilities, coded to indicate opinion type, current ratio, dividends/net income, firm size, investment cash flow/net

income, leverage, ROA, Operating cash flow/net income, retained earnings/total assets, sales/total assets[78] Current ratio, current liabilities/total assets, gross profit/total assets, inventories/working capital, (long-term debt + current

liabilities)/total assets, net income/gross profit, net income/net worth, ROA, net worth/net fixed assets, net worth/(net worth +long-term debt), quick assets/current liabilities, working capital/net worth[79] Break even point ratio, bonds payable, cash flow/interest expenses, cash flow/(previous years short-term loan), cash flow/short-

term loan, cash flow/total debt, cash flow/total loans, capital stock turnover, depreciation ratio, EBIT/sales, fixed assets/(stockholders equity + long-term liabilities), fixed assets turnover, fixed ratio, gross value added/(property, plant and equip-ment), gross value added/sales, gross value added/total assets, growth rate of tangible assets, interest coverage ratio, interestexpenses/total borrowings, interest expenses/total expenses, interest expenses/sales, inventories turnover, net income/sales, netincome/stockholders equity, ROA, net interest expenses/sales, operating assets turnover, ordinary income/ordinary expenses,ordinary income/sales, ordinary income/stockholders equity, ordinary income/total assets, payable turnover, productivity ofcapital, solvency ratio, stock holders equity/total assets, stock holders equity turnover, tangible assets turnover, total assetsturnover, (total borrowings + bonds payable)/total assets, variable cost/sales

[83] Current liabilities/current assets, funds provided by operations/total liabilities, log (total assets/GNP price-level index), netincome/total assets, one if total liabilities exceeds total assets, zero otherwise, one if net income was negative for the last twoyears, otherwise zero, total liabilities/total assets

[85] Cash flow/total loans, coverage debt, current assets/total assets, current assets-cash/total assets, net income/loans, ROA, netincome/total equity capital, reserves/loans

[86] Quick ratio, financial expenses/sales, fixed assets/(stockholders equity + long-term liabilities), gross value added/tangible fixedassets, gross value added/sales, growth rate of property, plant and equipment, growth rate of sales, growth potential, firmhistory, industry position, industry reputation, international competitive advantage, market niche/trend, operating assetsturnover, operating income/total assets, ordinary income/total assets, past payment record, personnel and staff hiring policy,pricing competitive advantage, profit perspective, quality of management, relationship between labour and capital, size,stockholders equity/total assets, technology development and quality innovation, total assets turnover, (totalborrowings + bonds payable)/total assets, working conditions and welfare facilities

[88] Current ratio, EBIT/interest expenses, EBIT/total assets, market value of equity/book value of debt, retained earnings/totalassets

[89] Cash at year end/total debt, cash flow/total debt, charge in inventories, charge in net financials, charge in net other assets andliability, charge in other current assets, charge in other current liabilities, charge in payables, charge in receivables, currentratio, current ratio trend, dividend, earnings trend, fixed coverage expenditure, long-term debt/net worth, net income/sales,

ROA, net investment flow, net operating flow, quick assets/current liabilities, quick assets/sales, sales trend (numberconsecutive years of sales decline, total debt/total assets, trend of cash flow/total debt, trend of net income/sales, trend of netincome/total assets, trend of working capital/sales, working capital/sales

[92] EBIT/total assets, market value of equity/total debt, retained earnings/total assets, sales/total assets, working capital/total assets[97] Cash/current liabilities, cash/total assets, cash flow/total assets, cash flow/total debt, current ratio, current assets/total assets,

current assets/total sales, current liabilities/equity, EBIT/total assets, equity/sales, inventory/sales, market value of equity/totalcapitalization, market value of equity/total debt, ROA, net income/total capitalization, quick assets/current liabilities, quickassets/total assets, quick assets/total sales, retained earnings/total assets, sales/total assets, total debt/total assets, workingcapital/sales, working capital/total assets

[98] GAAP (generally accepted accounting principals) net worth/total assets (GNWTA), repossessed assets/total assets (RATA),net income/gross income (NIGI), net income/total assets (NITA), cash securities/total assets (CSTA)


(continued on next page)


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the popular neural network architectures. Theydiffer in aspects including the type of learning, nodeconnection mechanism, the training algorithm,etc. Since, LVQ and Cascor are not very oftenused networks, their brief overview is presented as

follows:

LVQ has its origin in vector quantization (VQ),the main form of competitive learning neural net-work. In VQ, each of the competitive units corre-sponds to a cluster center and the error function isthe sum of squared euclidean distance between each

training case and the nearest center. LVQ is used to

Table 2 (continued)

Ref # Variables


[102] Quick ratio, current liabilities/total assets, financial expenses/sales, liquidity ratio, net income/stockholders equity, operatingincome/operating expenses, retained earnings/total assets, stock holders equity/total assets, value added/total cost

[104] Current ratio, EBIT/interest expenses, EBIT/total assets, market value of equity/book value of debt, retained earnings/totalassets

[106] Allowance for loan losses/total loans, asset growth, branch or unit bank, charter, core deposits/total assets, deposit insurance,earning assets/total assets, federal reserve bank member, gains (losses) from sale of securities/total assets, holding companyaffiliation, interest income/total assets, (non-interest expenses-salary)/total assets, non-interest income/total assets, non-performing assets/total assets, off balance sheet commitments/total assets, provision expenses/total loans, regional geographicalregion, salary/total assets, total equity/total assets, total interest expenses/total assets, total loans/total assets, total securities/total assets, volatile liabilities/total liabilities

[108] (Agriculture production and farm loans + real estate loans secured by farm land)/net loans and leases, (cash + US treasury andgovernment agency obligations)/total assets, capital/assets, commercial and industrial loans/net loans and leases, (federal fundssold + securities)/total assets, (interest and fees on loans + income from lease financing)/net loans and leases, loans toindividuals/net loan and leases, net charge offs/average loans, ROA, provision for loan loses/average loans, return on averageassets, total expenses/total assets, total income/total expenses, total interest paid on deposits/total deposits, total loans 90 days

or more past due/net loans and leases, total loans and leases/total assets, total loans and leases/total deposits, total non-accrualloans and leases/net loans and leases[110] (Agriculture production and farm loans + real estate loans secured by farm land)/net loans and leases, (cash + US treasury and

government agency obligations)/total assets, capital/assets, commercial and industrial loans/net loans and leases, (federal fundssold + securities)/total assets, (interest and fees on loans + income from lease financing)/net loans and leases, interest income/total assets, loans to individuals/net loan and leases, net charge offs/average loans, net income/total assets, provision for loanloses/average loans, real estate loans/(net loan & leases), return on average assets, total expenses/total assets, total interest paidon deposits/total deposits, total loans 90 days or more past due/net loans and leases, total loans and leases/total assets, totalloans and leases/total deposits, total non-accrual loans and leases/net loans and leases

[114] After tax profit/total assets, cash/total liabilities, working capital/operational expenditure[115] (Average tangible fixed assets-average construction in progress)/number of employees, current ratio, interests, discounts and

bond issue expenses/sales, interests, discount expenses/value added, liquid assets/current liabilities, non-operating expenses/sales, operating capital/number of employees, operating income/operating capital, ordinary income/sales, value added/operating capital

[116] Asset (loan) quality, earnings, liquidity, management, miscellaneous[119] (Cash + US treasury securities + federal funds sold and securities purchased under agreements to resell)/total assets, (certificate

of deposit over $100,000 + federal funds sold and securities purchased under agreements to repurchase)/total assets,commercial and industrial loans/total loans, doubtful loans/total capital, equity capital/total assets, (finance agricultureloans + farmers loans + real estate loans secured by farmland)/total assets, loans believed to be uncollectable/total capital,loans to individuals for household, family and other personal expenditure/total loans, net income/equity capital, ROA, realestate loans secured by 14 family residential properties/total loans, real estate loans secured by non-farm non-residentialproperties/total loans, substandard loans/total capital, total time and savings deposits/total deposits, total assets, total interestpaid on deposits/total deposits, total loans/(equity capital + reserve for loan losses), total loans/savings, total operatingexpenses/total assets


[122] Current liabilities/total debts, exploration expenses/total reserves, net cash flow/total assets, total debt/total assets, trend intotal reserves

[124] Debt/gross cash flow, earnings after abnormals /total assets, payout on operating profit before abnormals and tax, pre-taxprofit/total assets, working capital/total assets

[126] Current ratio, EBIT/total assets, market value of equity/total debt, retained earnings/total assets, sales/total assets, workingcapital/total assets

[128] Current ratio, ROA, total debt/total assets


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Table 3Other details of each paper

Ref # Bank/firm Source of data/country of origin #Samples Techniques used Ti

[1] Firms Korea, KIS (Korea Information Service)* 2400 DA, BPNN, RNN1, RNN2, HybridI, Hybrid II

19

[2] Banks USA, FDIC Annual report* 100 CNN, SONN, Fuzzy clustering 19[4] Firms Italy 3465 BPNN, LDA 19[5] Firms 111 ZETA analysis 19[6] Firms Spanish 5671 LDA, logit, multi-level perceptron,

Fuzzy rule base

[7] Firms USA 1160 BPNN with novel indicators 3 y[8] Firms Finnish 74 DA/DA, LA/LA, GA/BPNN, DA/

BPNN, LA/BPNN19

[9] Firms Korea 662 Auto-associative NN 19[10] Data used by Johnson and Wicherns[50]* LP to quadratic transformation,

QDF

[11] Firms [Standard and Poors COMPUSTATdatabase, Lexis/Nexis, Moodys IndustrialReport, Commerce Clearing Houses CapitalChange Reporting and The Wall StreetJournal, General Council of SEC, CRSP]*

237 BPNN, NPDA, logit 19

[12] Banks Texas, [FDIC (Federal Deposit Insurance

Corporation, Shesunhoff & Co)]*

2067 NN, logit 19

[13] Firms Data taken from UCI machine learningrepository*

37 Fuzzy rough-NN, Fuzzy-NN, crisp-NN

[14] Firms Data used by Greco et al.[39]* 39 Rough set 19[16] Firms Standard and Poors COMPUSTAT

database*

2085 CBR, logit 19

[18] Banks Turkish 40 PCA, MDA, logit, probit, IEWS(PCA + MDA + logit + Probit)

19

[19] Banks Belgium, [Chambers of Commerce, CD-RomNational Bank of Belgium]*

366 MSD (LP + DA), DEA, C5.0 19

[24] Firms Standard and Poors COMPUSTATdatabase*

150 Loan classification model from OLSand MDA

19

[26] Firms Greece, Greek 78 Rough set model using VCR 19[27] Law cases USA 102 BanXupport (IR + CBR)

[29] Firms Data used by Gentry et al.[34] 36 BPNN, logit [31] Firms Standard and Poors COMPUSTAT

database*

200 RPA, DA 19

[36] Firms Data used by Altman[3]* 66 Neuro-fuzzy and rough classifiers[37] Firms Greece, Greek industrial development bank

(ETEVA)*

39 Classical rough set and rough set withdominance relation

19

[38] Warehouses 12 Rough set approach with orderdomains

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Table 3 (continued)

Ref # Bank/firm Source of data/country of origin #Samples Techniques used Ti

[44] Banks USA, (Federal Financial InstitutionsExamination Council Form 031)*

176 Canonical correlation 19

[45] Firms Data used by Trippi and Turban[111]* 129 Ontogenic NN, DA, Odom & Shardamethod, Back Propagation,Perceptron, Athena

[46] Several Data used by Liang[68]* FILM, DA, ID3

[47] Firms Korea 542 DA, BPNN, CBR 19[48] Firms Korea 544 CBFS, DA, BPNN 19[51] Firms Australia, [Aspect Financial Pty Ltds

Financial Analysis Database, DatAnalysisDatabase, Huntleys Delisted CompanyDatabase, ASX market ComparativeAnalysis, Australian Securities andInvestment Commission (ASIC)]*

8241 Mixed logit model, MNL 19

[52] Banks Taiwan 24 DA, BPNN 20[53] Firms Standard and Poors COMPUSTAT

database*

50 MDA 19

[54] Firms Finnish 1500 Euclidean-SOM, Fisher metric-SOM [55] Firms Finnish, Kera Ltd* 1137 LDA, LVQ, SOM, RBF-SOM, K-

NN

[57] Banks USA 8977 IEWS (using logit), IEWS (usingTrait recognition)

19


282 Cascor, DA 19


34 FLDF, CBLP, MSD, LPC(combined method)


364 BPNN 19

[65] Firms Korea, Korean Stock Exchange* 166 MDA, ID3, MDA-assisted BPNN,ID3-assisted BPNN, SOFM-assistedBPNN

19

[66] Firms South korea, Korean Investors Service(KIS)*

168 BPNN, DA, SOM 19


88 MDA, MDA with gray zone, NN(perceptron)

19

[69] Firms UK, London Stock Exchange* 1133 Integration methods of DA, logit,Decision tree and BPNN

19

[70] Firms [Moodys Bond Record, Standard and PoorsStock Guide, CRSP tapes and Daily StockPrice Record]*

921 Recursive partitioning,bootstrapping, polytomous probit

[71] Banks USA, US commercial banks of FederalReserve System*

5700 Logistic regression 19

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[73] Firms USA, Compact Disclosure* 200 Rough set model, Recursivepartitioning model

19

[74] Firms USA, Compact Disclosure* 291 Rough set, GA, Rough set + GA 19[75] Firms USA, Compact Disclosure* 291 Rough sets, Auditor 19[78] Firms Greece 110 Fuzzy rule generator, LDA, QDA,

logit, probit5 a

[79] Firms Korea, Koreas largest credit guaranteeorganization*

1888 SVM, LDA, logit, BPNN 20

[80] Firms [1980 Bankruptcy Yearbook and Almanac,

Lexis/Nexis Database, Standard & PoorsCOMPUSTAT database]*

150 ICPB-MSD, LDA, MSD, ICPB-GA

and GA

19

[83] Firms [Moodys Manual, Standard & PoorsCOMPUSTAT database, 10-k financialstatements]*

2163 Logit 19

[85] Banks Spanish 66 BPNN, logit, MARS, C4.5, DA 19[86] Firms South Korea, Industrial bank of Korea* 2144 AHP-CBR, logit-CBR, weighted-

KNN, Pure-KNN19

[88] Firms [Bankruptcy Yearbook and Almanac, Lexis/Nexis database]*

100 GA-based BPNN, BPNN 19

[89] Banks andFirms

1. Belgian 2. Texas, Data used by Tam andKiang[108]*3. The data used by Rashadet al.[93]*

182 202 48 BPNN with Feature construction(FC), BPNN without FC

19

[92] Firms Moody Industrial Manuals* 129 BPNN, Athena, Perceptron 19

[97] Firms Standard and Poors COMPUSTAT* 301 Isotonic separation, DA, LPD,BPNN, Rough sets and OC1

19

[98] Firms Federal Home Loan Bank board quarterlytapes*

862 BPNN, logit 19

[100] Firms Moodys Industrial Manuals* 129 SOFM, LDA, MLP, Perceptron,Athena.

19

[101] Firms Moodys Industrial Manuals* 129 DA, BPNN, logit 19[102] Firms South Korea 528 GA 19[106] Banks USA 1741 MDA, BPNN, Regulators 19[107] Banks Texas 188 BPNN, Factor logistic, DA, K-NN,

ID319

[108] Banks Texas 202 LDA, logit, K-NN, ID3, feedforward NN, BPNN

19

[112] Firms UK DataStream and FT Excel companyResearch*

904 Quadratic interval logistic regression 19

[113] Firms Japan 114 BPNN, DA 19[124] Banks USA 3103 GenSoFNN-CRI (S), MCMAC 19[116] Firms Italy 4738 GA, LDA 19[118] Firms German 6667 GANN, GA, BPNN[119] Banks USA 1900 FA + logit 19[121] Firms Moodys Industrial Manual* 129 BPNN, DA 19

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solve classification problems. Each codebook vectoris assigned to one of the target classes. Each classmay have one or more codebook vectors. A caseis classified by finding the nearest codebook vectorand assigning the case to the class corresponding

to the codebook vector (see comp.ai.neural-netsFAQ, Part 1 of 7: Introduction) [56]. Fahlmanand Lebiere[28]introduced cascade correlation net-work, which adds units to the network during train-ing. Such a network is trained for a while. Then,without altering the existing weights, one or morenew hidden units are added to the network and thentraining resumes. The advantages of Cascor overbackpropagation are: (1) automatic determinationof a network topology resulting in good generaliza-tion (2) training time reduced by orders of magni-tude and (3) the ability to refine an existing

architecture to take into account new data withoutbeginning the training process all over again[62].

2.1.3. Decision trees

Decision trees form a part of machine learningan important area of artificial intelligence [33,91].A majority of the decision tree algorithms are usedfor solving classification problems. However, algo-rithms like CART (classification and regressiontrees) can be used for solving regression problemsalso. All these algorithms induce a binary tree on

the given training data, which in turn results in aset of ifthen rules. These rules can be used to solvethe classification or regression problem. A numberof algorithms are used for building decision treeincluding CHAID (Chi squared automatic interac-tion detection), CART, Quest and C5.0[94].

2.1.4. Rough sets

Rough set theory proposed by Pawlak [87] isbased on the assumption that with any object ofthe given universe there is some information associ-ated and objects characterized by similar informa-tion are indistinguishable or indiscernible. Theindiscernibility relation indicates that we are unableto deal with single objects but we have to considerclusters of indiscernible objects or equivalence clas-ses of the indiscernibility relation. In rough set the-ory, a pair of precise concepts viz., lower and theupper approximations replaces any vague concept.Approximations are two basic operations in therough set theory. Rough sets can be applied forinducing decision rules from data, to solve classifi-cation problems. The induced decision rules are cat-

egorized into exact and possible.Table3

(continued)

Re

f#

Ban

k/firm

Sourceo

fd

ata/countryo

forig

in

#S

amp

les

Tec

hn

iquesuse

d

Time

lineo

fdataset

[122]

Firms

USA

122

PNN

,PNN

withoutpattern

norma

lization,

FDA

,D

A

1984

1989

[123]

Firms

Austra

lia,C

D

Financ

ialAna

lysis*

44

CBR

(we

ightedNN

,Pu

reNN),DA

1991

2001

[126]

Firms

USA

220

BPNN

,Log

istic

1980

1991

[128]

Firms

Americana

ndNew

York

Stoc

kExc

hanges*

1681

Simp

lepro

bit

,bivariate

pro

bitan

d

unwe

ightedpro

bit

1972

1978

Note:

Inthethirdco

lumn*indicatessou

rceo

fdataan

d

indicatesthatthe

data

isnotava

ila

ble

.


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2.1.5. Case-based reasoning

Case-based reasoning (CBR), a branch of artifi-cial intelligence, is intuitively similar to the cognitiveprocess humans follow in problem solving [58].When people confront a new problem, they often

depend on past similar experiences and reuse ormodify solutions of these experiences to generate apossible answer for the problem at hand. The hall-mark of CBR is its capability to give an explanationfor its decision based on previous cases. Citing rele-vant previous experiences or cases is a way to justifya position[58] in human decision-making. Compre-hensibility of the decision is often crucial in solvingfinancial problems. When a company is identified asfailing, CBR can give examples of similar compa-nies that failed in the past as a justification for itsprediction. The heart of the CBR is the nearest

neighbour algorithm[96].

2.1.6. Support vector machines

Support vector machines (SVM) introduced byVapnik[115]use a linear model to implement non-linear class boundaries by mapping input vectorsnonlinearly into a high-dimensional feature space.In the new space, an optimal separating hyperplane(OSH) is constructed. The training examples thatare closest to the maximum margin hyperplane arecalled support vectors. All other training examples

are irrelevant for defining the binary class bound-aries[22,115]. SVM is simple enough to be analyzedmathematically. In this sense, SVM may serve as apromising alternative combining the strengths ofconventional statistical methods that are moretheory-driven and easy to analyze and machinelearning methods that are more data-driven, distri-bution-free and robust. Recently, the SVM has beenused to financial applications such as credit rating,time series prediction and insurance claim frauddetection. These studies reported that SVM wascomparable to and even outperformed other classi-fiers including BPNN, CBR, MDA and logit interms of generalization performance.

2.1.7. Data envelopment analysis

Data envelopment analysis (DEA) is a non-para-metric performance assessment methodology intro-duced by Cooper et al. [21]to measure the relativeefficiencies of organizational or decision-makingunits (DMUs). The DEA applies linear program-ming to observing inputs consumed and outputsproduced by decision-making units and con-

structs an efficient production frontier based on best

practices. Each DMUs efficiency is then measuredrelative to this frontier. In other words, DEAassesses the efficiency of each DMU relative to allthe DMUs in the sample, including itself. This rela-tive efficiency is calculated by obtaining the ratio of

the weighted sum of all outputs and the weightedsum of all inputs. The weights are selected so as toachieve Pareto optimality for each DMU. Anappealing aspect of DEA is that it does not requireprice or cost data. Also, the DEA is invariant toscaling of variables. The DEA helps to identify inef-ficient DMUs as well and amounts of inefficiency ofinputs and/or outputs.

2.1.8. Soft computing

The paradigm ofsoft computing or computational

intelligence refers to the seamless integration of dif-ferent, seemingly unrelated, intelligent technologiessuch as fuzzy logic, neural networks, genetic algo-rithms, machine learning (case-based reasoningand decision trees subsumed), rough set theoryand probabilistic reasoning in various permutationsand combinations to exploit their strengths. Thisterm was coined by Zadeh [125]in the early 1990sto distinguish these technologies from the conven-tional hard computing that is inspired by themathematical methodologies of the physical sci-

ences and focused upon precision, certainty andrigor, leaving little room for modeling error, judg-ment, ambiguity, or compromise. In contrast, softcomputing is driven by the idea that the gainsachieved by precision and certainty are frequentlynot justified by their costs, whereas the inexact com-putation, heuristic reasoning and subjective decisionmaking performed by human minds are adequateand sometimes superior for practical purposes inmany contexts. Soft computing views the humanmind as a role model and builds upon a mathemat-ical formalization of the cognitive processes thosehumans take for granted[125]. Within the soft com-puting paradigm, the predominant reason for thehybridization of intelligent technologies is that theyare found to be complementary rather than compet-itive in several aspects such as efficiency, fault andimprecision tolerance and learning from example[125]. Further, the resulting hybrid architecturestend to minimize the disadvantages of the individualtechnologies while maximizing their advantages.Some of the soft computing architectures employedare neurofuzzy, fuzzyneural, neurogenetic,

geneticfuzzy, neurofuzzygenetic, roughneuro,


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etc. Multi-classification systems or ensemble classifi-ers are also treated as soft computing systems.

3. Statistical techniques

Altman et al. [5] developed a new bankruptcyclassification model called Zeta analysis, whichincorporated comprehensive inputs. The data sam-ple consists of 111 firms with seven variables each.They found that the ZETA model outperformedalternative methods in terms of expected cost crite-ria. Classification accuracy of this model rangedfrom 96% for one period prior to bankruptcy to70% for five periods prior to bankruptcy. Martin[71] presented logistic regression to predict proba-bility of failure of banks based on the dataobtained from the Federal Reserve System, data

sample. Ohlson [83] employed the logit model topredict firm failure. The data was obtained fromMoodys Manual, Compustat data tapes and 10-K financial statements. The classification accuracyreported by him was 96.12%, 95.55% and 92.84%for prediction within one year, two years and oneor two years respectively. Dietrich and Kaplan[24] developed a simple three-variable linear modelto classify loan risks. He compared his model with(i) Altman model and (ii) Wilcox bankruptcy pre-diction [120] model and got better performance

over them. They used six independent variablesand one dependent variable suggested by individualexperts. The model gave better accuracy than previ-ous bankruptcy models in predicting the riskinessof loan.

Zmijewski [128] examined two estimation biasesfor financial distress models on non-randomsamples. The first bias results from oversamplingdistressed firms and falls under the topic of choice-based sample biases. The second results from usinga complete data sample selection criterion andfalls under the topic of sample selection biases.The data used in the study was obtained from theAmerican and New York Stock Exchanges. Thedata set consisted of estimation sample of 40 bank-rupt and 800 non-bankrupt firms and a predictionsample of 41 bankrupt and 800 non-bankrupt firms.The choice-based sample was examined usingunweighted probit and weighted exogenous samplemaximum likelihood. The sample selection biasissue was examined using simple probit and bivari-ate probit assessment. West [119] used the factoranalysis to create composite variables to describe

banks financial and operating characteristics. Data

was taken from Call & Income reports and exami-nation reports for 1900 commercial banks in somestates of USA. He demonstrated that his combinedmethod of factor analysis and logit estimation waspromising in evaluating banks condition. Karels

and Prakash [53] conducted a study in a threefoldmanner; (i) Investigated the normality condition offinancial ratios required by the MDA technique;(ii) when these ratios are non-normal, they con-structed ratios which are either multivariate normalor almost normal; (iii) using these ratios to comparethe prediction results of DA with that of other stud-ies. They used a random sample of 50 companiesobtained from the COMPUSTAT data tapes. Theyreported 96% classification rate for non-bankruptfirms and 54.5% for bankrupt firms.

Haslem et al. [44]determined the implication of

the foreign and domestic strategies reflected in thebalance sheets of US commercial banks. Also, theydetermined the impact of strategies on the profit-ability performance. For the analysis, they usedthe 1987 balance sheet data from the call reportsof 176 large US banks having both foreign anddomestic offices. They used canonical correlationanalysis to analyze balance sheet for the large andvery large bank samples and generated canonicalvariate scores. Kolari et al. [57] developed earlywarning system (EWS) based on logit analysis and

Trait recognition for large US banks. The logitmodel correctly classified over 96% of the banks 1year prior to failure and 95% of the banks 2 yearprior to failure. For developing trait recognitionmodel, they used half of the original sample.Because of this reduction in the sample size it hasdisadvantages over logit model. In both 1 yearand 2 year prior to failure data classification accu-racy of trait model was 100%. It was concluded thattrait recognition outperformed logit model in termsof type-I and type-II errors.

Recently, Jones and Hensher [51] presentedmixed logit model for firm distress prediction andcompared it with multinomial logit models(MNL). They modeled financial distress problemin three states viz., state 0: non-failed firms; state1: insolvent firms, state 2: firms which filed for bank-ruptcy. They developed two samples for model esti-mation and validation. The results are too detailedto present here. They concluded that mixed logitobtained substantially better predictive accuracythan multinomial logit models. Canbas et al. [18]proposed an integrated early warning system

(IEWS) by combining DA, logistic regression, pro-


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bit and principal component analysis (PCA), thathelped in examination and detection of banks withserious problems. PCA explored three financialcomponents, which significantly explained thechanges in the financial condition of banks. With

these three factors they employed DA, logisticregression and probit models. Then, by combiningall these together they constructed an IEWS. Theyused the data of Turkish banks available in website(http://www.tbb.org.tr/english/bulten/yillik/2000/ratios.xls). The results are too elaborate to presenthere. They concluded that IEWS has more predic-tive ability than other models.

4. Neural networks

This section reviews the papers where different

topologies of neural networks (NN) are proposedand compared with other techniques. This sectionis split into three sub sections covering the applica-tions of (i) back propagation trained NN (BPNN),(ii) self-organizing feature map (SOM) and (iii)other NN topologies such as probabilistic NN, autoassociative NN and cascade correlation NN.

4.1. Back propagation trained neural network

(BPNN)

Tam[107]employed BPNN for bankruptcy pre-diction. Data were obtained from Texas banks, oneyear and two years prior to failure. He selected thevariables based on CAMEL criteria of FDIC. Heshowed that BPNN offered better predictive accu-racy than other methods viz., DA, factor-logistic,K-nearest neighbour (K-NN) and ID3 [77]. Tamand Kiang [108] compared the performance of (i)LDA, (ii) logistic regression, (iii) K-NN, (iv) ID3,(v) feedforward NN (net0) and (vi) BPNN (net10)on bankruptcy prediction problems. BPNN outper-formed other techniques for one-year prior trainingsample, whereas for two-year prior training sampleDA outperformed others. However, BPNN outper-formed others in both the one-year prior and thetwo-year prior holdout samples. In jackknifemethod [61] also, BPNN outperformed others inboth the one-year prior and the two-year prior hold-out samples. So, with the evidence of jackknifemethod, they concluded that NN outperformedthe DA methods.

Salchenberger et al. [98] presented a BPNNto predict the probability of failure for savings

and loan associations (S&Ls). They compared its

performance with a logistic model. They considered29 variables from the CAMEL categories and per-formed stepwise regression that identified five vari-ables. Results are too detailed to present here.They concluded that BPNN outperformed logistic

regression. Sharda and Wilson [101] compared theBPNN with MDA based on resampling technique.They used Altmans five variables. They usedBPNN with five input nodes, 10 hidden nodes andtwo output nodes. They concluded that BPNN out-performed DA in all cases. Fletcher and Goss [29]used the BPNN for predicting bankruptcy of firmsand compared it with logistic regression. Theyemployed v-fold cross-validation technique. Thedata of 36 companies was drawn from Gentryet al. [34]. They used three independent variables.BPNN prediction performance was 82.4% whereas

logistic regression produced only 77%. Altmanet al. [4] compared the performance of LDA withBPNN in distress classification. They used 10 finan-cial ratios. The data sample consisted of three typesof firms viz., (i) healthy, (ii) unsound and (iii) vul-nerable. Three sample data sets were used for thisstudy. They obtained best results with BPNN hav-ing three layers: initial hidden layer of 10 neurons,second hidden layer with four neurons and an out-put layer of one neuron. They concluded thatLDA marginally outperformed BPNN.

Wilson and Sharda[121]compared the predictiveaccuracy of BPNN with that of DA. They used Alt-man[3] variables. They concluded that BPNN out-performed other methods over all test samples.Tsukuda and Baba [113] performed the predictionof bankruptcy using BPNN with one hidden layerand concluded that BPNN outperformed the DA.Leshno and Spector [67] compared various NNmodels and DA and explained their predictioncapabilities in terms of data span, learning tech-nique and number of iterations. This study usedthe perceptron like network for input features oftwo types viz., (i) functional expansion (FE), (ii)

joint activation (JA) and investigated their effecton generalization. They used 41 financial ratiosincluding Altman[3]variables. They concluded thatNN outperformed the Z-score model. Rahimianet al. [92]compared the performance of (i) BPNN,(ii) Athena, an entropy-based neural network and(iii) single layer perceptron on the bankruptcy pre-diction problem. They compared them with Odomand Shardas [82]BPNN and discriminant analysisalso. The accuracies obtained on the test data were

(i) discriminant analysis produced 74.54%, (ii)

http://www.tbb.org.tr/english/bulten/yillik/2000/ratios.xlshttp://www.tbb.org.tr/english/bulten/yillik/2000/ratios.xlshttp://www.tbb.org.tr/english/bulten/yillik/2000/ratios.xlshttp://www.tbb.org.tr/english/bulten/yillik/2000/ratios.xls

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Odom and Shardas test produced 81.81%, (iii)Athena yeilded 81.81%, (iv) perceptron yielded81.81% and (v) BPNN produced 81.81%. TheBPNN implemented in this study outperformedOdom and Shardas [82] BPNN in terms of speed.

Barniv et al. [11] compared BPNN, multi-stateordered logit and non-parametric multiple discrimi-nant analysis (NPDA). They developed a model forclassifying firms into three states viz. acquired,emerging and liquidated. They designed two modelsviz., (i) twelve variable model and (ii) five variablemodel. These two models outperformed Ohlsons[83] nine variable model. They concluded thatBPNN outperformed NPDA and logit models. Bell[12]compared logistic regression and BPNN in pre-dicting bank failures. In this study, he used 28 can-didate predictor variables. The architecture of

BPNN was 12 input nodes, six hidden nodes andone output node. He concluded that neither thelogit nor the BPNN model dominated the other interms of predictive ability. But, for complex decisionprocesses BPNN was found to be better.

Piramuthu et al. [89] designed a method calledfeature construction (FC) and used it with BPNNfor bankruptcy prediction. They used the BelgianBankruptcy data of 182 banks, Tam and Kiang[108] data and Rashid and EI-Sheshai [93] data of48 banks. They concluded that BPNN with FC out-

performed the plain BPNN in all datasets. Zhanget al. [126] used generalized reducing gradient(GRG2) trained three-layered NN for bankruptcyprediction. They used v-fold cross-validation tech-nique for testing. They reported that overall classifi-cation rates of GRG2 trained NN ranged from77.27% to 84.09% whereas that for logistic regres-sion ranged from 75% to 81.82%. They concludedthat GRG2 trained NN outperformed logisticregression. Atiya [7] reviewed the applications ofNN in bankruptcy prediction and developed anNN. He developed novel indicators for the NN, tak-ing cue from Merton[76]. For the study he collecteddata from defaulted and solvent US firms. Hereported a prediction accuracy of 84.52% for thein-sample set and 81.46% for the out-of-sampleset. He showed that the use of the indicators in addi-tion to financial ratios provided significantimprovement.

Swicegood and Clark [106] compared DA,BPNN and human judgment in predicting bank fail-ures. The variables were taken from the bank callreports. Overall, MDA model correctly classified

86.4% and 79.5% of regional and community banks

respectively. However, BPNN model correctly clas-sified 81.4% and 78.25% of regional and communitybanks. They concluded that BPNN outperformedother two models in identifying under performancebanks. Lam[64]integrated fundamental and techni-

cal analysis in BPNN for financial performance pre-diction. The predictors included 16 financial and 11macroeconomic variables. She concluded thatBPNN significantly outperformed the minimumbenchmark based on highly diversified investmentstrategy. Also, incorporation of previous yearsfinancial data in the input vector for BPNN couldsignificantly increase the return level, thereby, dem-onstrating the benefits of integrating fundamentalanalysis with technical analysis via BPNN. She alsoextracted rules from trained neural network andfound that they outperformed the neural networks

per se. Further, they performed as accurately asthe maximum benchmark. Lee et al. [66]comparedBPNN with self-organizing feature map (SOM),DA and logistic regressions. The data sample con-sisted of 168 Korean firms taken from the Securityand Exchange Commission (SEC) filings stored inan on-line database of the Korea Investors Service(KIS) Inc. (www.kisrating.com). The fourfoldcross-validation testing was used for all the models.The results are too detailed to present here. Theyconcluded that the BPNN outperformed the all

other techniques.

4.2. Self-organizing maps (SOM)

Lee et al.[65]proposed three hybrid BPNN viz.,(i) MDA-assisted BPNN (ii) ID3-assisted BPNNand (iii) SOM-assisted BPNN for predicting bank-ruptcy in firms. The data of 166 firms is taken fromthe Korea Stock exchange. They selected 57 finan-cial variables. They concluded that hybrid neuralnetwork models performed better than MDA andID3. Serrano-Cinca [100] compared the perfor-mance of SOM with LDA and BPNN in financialdiagnosis. The data set consisted of Altmans [3]variables. The architecture of SOM used was 4 inputnodes and 144 output nodes arranged in a 12 12square grid in order to accommodate 74 patternsin data sample. He proposed two hybrid neural sys-tems viz., (i) a combination of LDA with SOM,where LDA calculated the Z-score for each firm,which was superimposed onto SOM to obtain iso-solvent regions, (ii) a combination of BPNN withSOM. The LDA obtained 74.5%, while other mod-

els such as Rahimian et al.s MLP[92], Odom and

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Shardas MLP [82], Perceptron model, AthenaModel and his own MLP obtained 81.8%. The pro-posed system outscored Z-score analysis in provid-ing intuitive visual graphics that give informationon the risk of bankruptcy, the financial characteris-

tics of firm and that type of firm it is similar to.Kiviluoto[55]used SOM and proposed its variantsfor firm bankruptcy prediction. He compared threedifferent SOM-based classifiers viz., SOM-1, SOM-2and RBF-SOM hybrid with LDA, learning vectorquantization (LVQ) and K-NN. The parametersfor each classifier were determined using v-foldcross-validation technique. He modified the LVQalgorithm to accommodate the NeymanPearsonclassification criteria. This NeymanPearson LVQnot only speeded up the convergence but alsoincreased the classification accuracy. He used the

data segment from Kera Ltds customer companiesfor the study. He concluded that NeymanPearsonLVQ is more useful than one minimizing the totalnumber of misclassifications. He concluded thatother classifiers outperformed SOM-1. He also con-cluded that RBF-SOM performed slightly betterthan other classifiers. Kaski et al. [54] introducedFisher information matrix based metric and imple-mented SOM with it. They used the new methodto understand the non-linear dependencies betweenbankruptcies and financial indicators. The depen-

dencies were converted into a metric of the inputspace and the SOM was used to visualize thedependencies in a concise form. They obtained 23financial indicators from Finnish small and med-ium-sized enterprises. They computed the accuracyof SOMs in the Euclidean metric (SOM-E) and inthe Fisher metric (SOM-F) in representing the prob-ability of bankruptcy, measured by the likelihood ofdata at the location of the best matching SOMunits. He concluded that the SOM-F performed bet-ter than the SOM-E.

4.3. Other neural network topologies

Lacher et al. [62] proposed a cascade-correlationneural network (Cascor) for classifying financialhealth of a firm. Altmans five financial ratios wereused. Data was collected from Standard and PoorsCOMPUSTAT financial database. He comparedthe performance of the Cascor model with that ofAltman Z-score model. They concluded that theCascor model consistently yielded higher overallclassification rates. Yang et al. [122] proposed

PNN without pattern normalization and Fisher

discriminant analysis (FDA) to solve bankruptcyprediction problem. They compared the originalPNN and PNN without pattern normalization(PNN*) and FDA with DA and BPNN. The Dataused was taken from Platt et al. [90]. The first four

ratios were deflated to remove the differences inratio values over time caused by fluctuations inrelated factors. The results are too detailed to pres-ent here. They concluded that the PNN* and BPNNwith non-deflated data achieved better classificationrates. FDA produced better classification resultswith deflated data. They found that deflationimproved the discrimination ability of some of theprediction models as observed in [90]. Baek andCho [9] proposed the auto-associative neural net-work (AANN) for Korean firm bankruptcy predic-tion. They trained the AANN with only solvent

firms data. Then they applied the test data contain-ing both solvent and insolvent firms. So, any solventfirm data that shared common characteristics withthe training data resulted in small error at the out-put layer while the bankrupt firms data resulted ina large error at the output layer. AANN yieldedclassification rates of 80.45% for solvent and50.6% for defaulted firms. However, the 2-classBPNN produced classification rates of 79.26% forsolvent and 24.1% for defaulted firms. Therefore,they concluded that AANN outperformed 2-class

BPNN.

5. Case-based reasoning techniques

Bryant [16] designed a CBR system for bank-ruptcy prediction. He compared it with Ohlsons[83]logit model. CBR cluster trees were created withthree case libraries viz., model-I, model-II andmodel-III. They consisted of 25 financial variablesfor one year, two year and three years data. Theresults reported by him are too elaborate to mentionhere. He concluded that logit outperformed CBR interms of less Type-I accuracy. Jo et al. [47] usedMDA, CBR and BPNN to predict bankruptcy.They considered the data taken from Korean firms.Variables were selected using the dimension reduc-tion techniques such as stepwise selection andt-test.The average hit ratio of DA, BPNN and CBR was82.22%, 83.79% and 81.52%, respectively. They con-cluded that BPNN outperformed DA and CBR andDA outperformed CBR. Park and Han [86] pro-posed analytic reasoning model called the K-NNwith analytic hierarchy process (AHP) feature

weight approach for bankruptcy prediction. They


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proposed CBR for indexing and retrieving similarcases. The AHP-weighted K-NN was comparedwith pure K-NN algorithm. For this study, theyused the data obtained from Industrial Bank ofKorea. They used both financial and non-financial

variables. The classification accuracy of pure K-NN approach was 68.3% whereas the hybridsLogit-CBR and AHP-K-NN-CBR produced79.2% and 83.0%, respectively. They concluded thatweighted K-NN hybrid model outperformed othermodels.

Yip[123]used CBR with K-NN to predict Aus-tralian firm business failure. She used the statisticalevaluations for assigning the relevancy of attributesin the retrieval phase of algorithm. She comparedthe performance of CBR + K-NN with that ofDA. The overall accuracy of CBR with weighted

K-NN, CBR with pure K-NN and DA were90.9%, 79.5% and 86.4%, respectively. She con-cluded that CBR with weighted K-NN was betterthan DA.

6. Decision trees

In this section, we review the works reported onthe application of decision trees. Decision trees userecursive partitioning algorithm to induce rules ona given data set. Marais et al. [70] proposed recur-

sive partitioning algorithm (RPA) for predictingbankruptcy in firms. They used (i) recursive parti-tioning technique and (ii) bootstrapping. Theyapplied polytomous probit and recursive partition-ing to the data sample. The results reported aretoo detailed results to be presented here. However,it can be inferred that when all the variables wereused, polytomous probit outperformed recursivepartitioning in terms of expected misclassificationrates in both resubstitution and bootstrap methods.Frydman et al. [31] presented the application ofRPA to bankruptcy prediction and compared itwith the DA and the analysis was carried out formisclassification cost of C12 ranging from 1 to 70,where C12denotes the cost of misclassifying samplebelonging to group 1 to group 2. They constructedtwo variants of discriminant functions viz., DA1and DA2 and compared them with two RPA mod-els viz., (i) RPA1 with relatively complex tree and(ii) RPA2 with smallest v-fold cross-validation risk.RPA1 model outperformed DA1 and DA2 modelsfor all costs. Also, RPA2 tree turned out to be subtree of RPA1 tree for every cost. They showed that

RPA2 had larger resubstitution risk.

7. Evolutionary approaches

Varetto[116]employed a genetic algorithm (GA)for bankruptcy prediction and compared its perfor-mance with that of LDA. He conducted the study

for: (i) one year prior to bankruptcy data and (ii)three years prior to bankruptcy data. He reportedthat for case (i), the genetic linear function yielded92% classification rate for bankrupt companies andLDA yielded 90.1%. However, in case (ii), heobserved that LDA outperformed the genetic linearfunction in the case of sound companies. He alsoinferred that the LDA has a higher stability and gen-eralization power. Nanda and Pendharkar [80]incorporated misclassification cost matrix into anevolutionary classification system. Using simulatedand real-life bankruptcy data, they compared the

proposed method with LDA, a goal programmingand a GA-based classification without the asymmet-ric misclassification costs. For bankruptcy trainingset the classification accuracy of integrated cost pref-erence based mininized sum of deviations (ICPB-MSD) and integrated cost preference based GA(ICPB-GA) outperformed LDA, MSD and GA.For simulated holdout set the ICPB-GA outper-formed others. They concluded that the ICPB-MSD or ICPB-GA might be promising whencompared to traditional MSD or GA. Shin and

Lee [102] also proposed a GA-based approach forbankruptcy prediction. The rules generated by GAwere easily understood and could be used as expertsystems. Data used contained 528 firms. The fiverules generated by GA got 80.8% accuracy. Theyconcluded that GA could successfully learn linearrelationship among input variables.

8. Operational research

Banks and Prakash[10]proposed the linear pro-gramming heuristic to a quadratic transformationof data to predict firm bankruptcy prediction. Qua-dratic discriminant function (QDF) got three mis-classifications whereas Johnson and Wichern [50]got 46. They concluded that the quadratic transfor-mation method outperformed the QDF. Lam andMoy[63]compared different DA methods and pro-posed the their combination to predict the classifica-tion of new observations. For testing this hybridtechnique, they used simulation experiment. Dis-criminant analyses taken for this study were FLDF(Fisher linear discriminant analysis), cluster-based

LP (CBLP) and MSD (minimized sum of devia-


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tions). Their simulation generated data from con-taminated multivariate normal distribution for thefirst 24 cases and for remaining 10 cases containednon-contaminated data to test the robustness ofLPC, which combined classification results of differ-

ent DA. Their combined method outperformedother DA methods. LPC was reformulated as amixed-integer programming model, which mini-mized weighted number of misclassifications. Cielenet al. [19]compared the performance of minimizedsum of deviations (MSD), data envelopment analy-sis (DEA) model and a rule induction (C5.0) modelon bankruptcy prediction problem. Here MSD wasa combination of linear programming (LP) and DA.The dataset was taken from National Bank ofBelgium. The MSD, DEA and C5.0, obtained clas-sification rates of 78.9%, 86.4% and 85.5% respec-

tively. They concluded that DEA outperformedC5.0 and MSD model. Kao and Liu[52]formulateda DEA model for interval data for evaluating theperformance of banks. This study made advancepredictions of the performance of 24 Taiwan banksbased on uncertain financial data presented inranges. They presented the prediction of efficiencyscores also in ranges. Among 24 banks, two banksgot the smallest predictive efficiency scores of0.7358 and 0.7584 because these two banks sufferedfrom Asian financial crisis and had many bad debts.

They showed that DEA predicted the bank perfor-mance based on their financial forecasts.

9. Rough sets

Greco et al. [38] proposed a new rough setapproach for solving bankruptcy prediction prob-lem considering the criteria of attributes withordered domains. This approach was similar tothe original rough set analysis in that it used theapproximation of partitioning the objects in somepre-defined category. However, it employed bothdominance relation and indiscernibility relation.They represented warehouse making loss with classCL1 and warehouse making profit with class CL2.The classical rough set approach got the accuracyof approximation of 0.6 and 0.7 for CL1 and CL2respectively and the quality of classification was0.83. However, the proposed approach got the accu-racy of approximation of 0.33 and 0.6 for CL1andCL2 respectively and the quality of classificationwas 0.67. They concluded that the proposedapproach showed improvements over the original

rough set analysis. This improvement be seen by

the smaller reduct of {A1, A4} obtained by the pro-posed approach as against the reduct {A1, A2, A3and A4} obtained by original rough set analysisobtained. The decision rules obtained from the pro-posed approach gave more synthetic representation

of knowledge contained in the information.Greco et al. [37] presented a new rough setmethod based on approximation of a given partitionof set of firms into pre-defined and ordered catego-ries of risk by means of dominance relation in placeof indiscernibility relation for the evaluation ofbankruptcy in firms. Dominance relation wasproposed in place of indiscernibility relation in[3943,103]. The classical approach based on indis-cernibility relation is applied to classification prob-lems with regular attributes and preferentiallynon-ordered decision classes, whereas, the domi-

nance-based rough set approach handles prefer-ence-ordered domains of attributes (criteria) andpreference-ordered decision classes. The domi-nance-based rough set approach performs very wellon financial data. It is also the only data miningapproach handling preference order in data. Thedata set was obtained from Greek industrial devel-opment bank (ETEVA). The data sample was clas-sified into (i) unacceptable, (ii) uncertainty and (iii)acceptable. They compared classical rough set withtheir proposed method. They showed that the pro-

posed method gave smaller number of reducts thanclassical rough set approach based on indiscernibil-ity. The quality of the approximation obtained byclassical rough set approach and the proposedmethod based on dominance were 1 and 0.949respectively. Also, the decision rules obtained fromthe approximation by

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