A hybrid approach of DEA, rough set and support vector machines for business failure prediction

A hybrid approach of DEA,rough set and support vector machines for business failure predictionChing-Chiang Yeh a ,Der-Jang Chi b,*,Ming-Fu Hsu caDepartment of Business Administration,National Taipei College of Business,Taipei,Taiwan,ROC bDepartment of Accounting,Chinese Culture University,Taipei 11114,Taiwan,ROC cDepartment of International Business Studies,National Chi Nan University,Nantou County,Taiwan,ROCa r t i c l e i n f o Keywords:Business failure Financial ratios DEARough setSupport vector machinesa b s t r a c tThe prediction of business failure is an important and challenging issue that has served as the impetus for many academic studies over the past three decades.While the efficiency of a corporation’s management is generally acknowledged to be a key contributor to corporation’s bankrupt,it is usually excluded from early prediction models.The objective of the study is to use efficiency as predictive variables with a pro-posed novel model to integrate rough set theory (RST)with support vector machines (SVM)technique to increase the accuracy of the prediction of business failure.In the proposed method (RST–SVM),data envelopment analysis (DEA)is employed as a tool to evaluate the input/output efficiency.Furthermore,by RST approach,the redundant attributes in multi-attribute information table can be reduced,which showed that the number of independent variables was reduced with no information loss,is utilized as a preprocessor to improve business failure prediction capability by SVM.The effectiveness of the meth-odology was verified by experiments comparing back-propagation neural networks (BPN)approach with the hybrid approach (RST–BPN).The results shows that DEA do provide valuable information in business failure predictions and the proposed RST–SVM model provides better classification results than RST–BPN model,no matter when only considering financial ratios or the model including both financial ratios and DEA.Ó2009Elsevier Ltd.All rights reserved.1.IntroductionThe prediction of business failure is an important and challeng-ing issue that has served as the impetus for many academic studies over the past three decades (Altman,1968;Beaver,1966;Bryant,1997;Ohlson,1980).Business failure is a general term and,accord-ing to a widespread definition,is the situation that a firm cannot pay lenders,preferred stock shareholders,suppliers,etc.,or a bill is overdrawn,or the firm is bankrupt according to the law (Ahn,Cho,&Kim,2000).Widely identified causes and symptoms of busi-ness failure include poor management,autocratic leadership and difficulties in operating successfully in the market.As the world’s economy has been experiencing severe challenges during the past decade,more and more companies,no matter large or small,are facing the problems of filing bankruptcy.Thus,accurate business failure prediction models have drawn serious attention from both researchers and practitioners aiming to provide on time signalsfor better investment and government decisions with timely warnings.Many different useful techniques have already been investi-gated in the course of comparative studies related in several re-view articles (Altman,1984;Dimitras,Zanakis,&Zopounidis,1996;Jones,1987;Keasey &Watson,1991;Scott,1981;Zavgren,1983)in order to solve the problems involved during the evalua-tion process.Recently,Kumar and Ravi (2007)gave a complete review of methods used for the prediction of business failure and of new trends in this area.Basically,the business failure prediction models use appropriate independent variables to ‘‘pre-dict”a company is a healthy company or a bankrupt one.There-fore,the business failure prediction problems are in the scope of the more general and widely discussed discrimination and classi-fication problems (Johnson &Wichern,2002).However,while these well-established techniques are there to solve business fail-ure prediction problems and applications,two main problems arise.First,after Beaver (1966)and Altman (1968)used the financial ratios methodology in conducting business failure predictions,most of the studies only considered financial ratios as independent (input)variables.Although financial ratios,originated in a corpora-tion’s financial statements,can reflect some characteristics of a0957-4174/$-see front matter Ó2009Elsevier Ltd.All rights reserved.doi:10.1016/j.eswa.2009.06.088*Corresponding author.Address:Department of Accounting,Chinese Culture University,55,Hwa-Kang Road,Yang-Ming-Shan,Taipei 11114,Taiwan,ROC.Tel.:+886228610511x35505;fax:+886228614177.E-mail address:djchi@ (D.-J.Chi).Expert Systems with Applications 37(2010)1535–1541Contents lists available at ScienceDirectExpert Systems with Applicationsjournal homepag e:/locate/eswacorporation from various aspects to a certain extent.While the efficiency of a corporation’s management is generally acknowl-edged to be a key contributor to corporation’s bankrupt(Gestel et al.,2006;Seballos&Thomson,1990;Secrist,1938),it is usually excluded from early prediction models.Therefore,in this study,we believe efficiency which reflects the status of the management of a corporation in business failure predictions will be decisive factors affecting the predictive capability.For a typical efficiency measurements,for example,research on operational efficiency—the most widely studied efficiency issue—assumes the resources of a corporation as inputs(e.g.,personnel, technology,space,etc.)and some measurable form of the services provided as output(e.g.,number of accounts serviced or loans and other transactions processed,etc.).However,it is hard to evaluate the efficiency of a corporation directly from itsfinancial state-ments.An approach known as data envelopment analysis(DEA) may serve to offer useful insights into the manner by incorporating multiple inputs and outputs;DEA is able to provide measures for the efficiency of a corporation.Secondly,early studies of business failure prediction used sta-tistical techniques such as univariate statistical methods,multiple discriminant analysis(MDA),linear probability models,and logit and probit analysis have mainly been used for business classifica-tion problems(Altman,1968;Altman,Haldeman,&Narayanan, 1977;Collins&Green,1972).These conventional statistical meth-ods,however,have some restrictive assumptions such as the line-arity,normality and independence among predictor or input variables.Considering that the violation of these assumptions for independent variables frequently occurs withfinancial data(Dea-kin,1972),the methods can have limitations to obtain the effec-tiveness and validity.Artificial intelligence approaches that are less vulnerable to these assumptions,such as inductive learning,Neural networks (NN)can be alternative methodologies for classification problems to which traditional statistical methods have long been applied. NN have shown to have better predictive capability than MDA and logistic regression in business failure prediction problems (Coleman,Graettinger,&Lawrence,1991,Rahimian Salchengerger, Cinar,&Lash,1993,Salchengerger et al.,1992,Sharda&Wilson, 1996,Tam&Kiang,1992,Wilson&Sharda,1994,Zhang,Hu,Pat-uwo,&Indro,1999).Recently,support vector machines(SVM), developed by Vapnik(1995),have gained popularity due to many attractive features and excellent generalization performance on a wide range of problems.Also,SVM embody the structural risk min-imization principle(SRM),which has been shown to be superior to traditional empirical risk minimization principle(ERM)employed by conventional neural networks.It has been demonstrated by Min and Lee(2005)that SVM outperform NN,MDA and logistic regression in business failure prediction.While there are several arguments that variable selection,also called feature selection,is a fundamental problem that has signif-icant impact on the prediction accuracy of the models.Many meth-ods have been developed to create the best preparation for data inputs.For doing good classification process in SVM,the prepara-tion of data inputs for classifier needs special treatment to guaran-tee the good performance in the classifier.It is therefore not surprising that much research has been done on dimensionality reduction(Dash&Liu,1997;Kira&Rendell,1992;Langley, 1994).A technique that can reduce dimensionality using informa-tion contained within the data set and preserving the meaning of the features is clearly desirable.Rough set theory(RST)can be used as such a tool to discover data dependencies and reduce the num-ber of attributes contained in a dataset by purely structural meth-ods(Pawlak,1991),have successfully been applied to real world classification problems(Ahn et al.,2000;Siegel,de Korvin,&Omer, 1993;Slowinski&Zopounidis,1995).The objective of the study is using efficiency as predictive vari-ables and proposed a novel model to integrate RST with SVM tech-nique,named RST–SVM,to increase the accuracy for the prediction of business failure.By RST approach,the redundant attributes in multi-attribute information table can be reduced,which showed that the number of independent variables was reduced with no information loss,is utilized as a preprocessor to improve business failure prediction capability by SVM.In thefirst stage,RST is se-lected for doing variable selection because of its reliability to ob-tain the significant independent variables.The second stage of the study will use the obtained significant independent variables from RST as inputs of SVM models.The obtained results can then be compared to see whether the one including efficiency variable will give better classification accuracy or not.In the proposed method,DEA is employed as a tool to evaluate the input/output efficiency.The effectiveness of the methodology was verified by experiments comparing back-propagation neural networks(BPN) approach with the hybrid approach(RST–BPN).This paper is organized as follows.We will give a brief review of the DEA model used to evaluate the efficiency of a corporation in Section2.Section3describes classification techniques used in pre-vious researches concerned with our paper:RST and SVM,respec-tively.In Section4,the proposed data preprocessing algorithm by RST and hybrid models is described.In Section5,we analyze and compare the results of each model.Finally,discussion and conclu-sions are provided in Section6.ing DEA for evaluating the efficienciesData envelopment analysis(DEA)is an evaluation tool for deci-sion making units(DMUs)and it solves many decision-making problems by integrating multiple inputs and outputs simulta-neously.DEA is a non-parametric data analytic technique that is extensively used by various research communities(e.g.,Hong, Ha,Shin,Park,&Kim,1999;Seol,Choi,Park,&Park,2007;Sohn &Moon,2004).The basic ideas behind DEA date back to Farrell (1957)but the recent series of discussions started with the article by Charnes,Cooper,and Rhodes(1978).We give very briefly the salient features of DEA.More detailed information can be obtained elsewhere(Banker,Charnes,&Cooper,1984;Charnes,Cooper,Le-win,&Seiford,1993).The DEA ration form,proposed by Charnes,Cooper and Rhodes (CCR)(1978),is designed to measure the relative efficiency or pro-ductivity of a specific DMUk.The DEA formulation is given as fol-lows.Suppose that there is a set of n DMUs to be analyzed,each of which uses m common inputs and s common outputs.Let k (k=1,...,n)denote the DMU whose relative efficiency or produc-tivity is to be maximized.Maximize h k¼P sr¼1u rk Y rkP mi¼1v ik X ikSubject toP sr¼1u r Y rjP mi¼1v i X ij61ð1Þu r;v i P0i¼1;2;...;mr¼1;2;...;sj¼1;2;...;nwhere u rk is the variable weights of given to the r th output of the k th DMU,v ik is the variable weights of given to the i th input of the k th DMU,u rk and v ik are decision variables determining the rel-ative efficiency of DMU k,Y rj is the r th output of the j th DMU,and X ij is the i th input of the j th DMU.It also assumes that all Y rj and X ij are positive.h k is the efficiency score and is less than or equal to1. When efficiency score of h k is1,DMU k is called the efficient frontier.1536 C.-C.Yeh et al./Expert Systems with Applications37(2010)1535–1541There are two types of CCR models.One version is input orientedmodel,which minimizes the inputs,and the other is output ori-ented model maximizing the outputs.In this paper,we apply theoutput oriented CCR model since we focus on maximizing the mul-tiple outputs.3.Rough sets and support vector machines3.1.Basic concepts of rough setsRough sets theory(RST)is a machine-learning method,which isintroduced by Pawlak(1991)in the early1980s,has proved to be apowerful tool for uncertainty and has been applied to data reduc-tion,rule extraction,data mining and granularity computation.Here,we illustrate only the relevant basic ideas of RST that are rel-evant to the present work.By an information system we understand the4-tupleS=ðU;A;V;fÞ,where U is afinite set of objects,called the universe,A is afinite set of attributes,V¼U a2A V a is a domain of attribute a,and f:UÂA!V is called an information function such thatfðx;aÞ2v a,for8a2A;8x2U.In the classification problems,an information system is also seen as a decision table assuming thatA¼C[D and C\D¼/,where C a set of condition attributesand D is a set of decision attributes.Let S¼ðU;A;V;fÞbe an information system,every P#A gener-ates an indiscernibility relation INDðPÞon U,which is defined asfollows:INDðPÞ¼fðx;yÞ2UÂU:fðy;aÞ;8a2p gð2ÞU=INDðPÞ¼f c1;c2;...;c k g is a partition of U by P,every C i is an equivalence class.For8x2U the equivalence class of x in relation to U=INDðPÞis defined as follows:½xU=INDðPÞ¼f y2U:fðy;aÞ¼fðx;aÞ;8a2P gð3ÞLet P#A and X#U.The P-lower approximation of x(denoted by PÃðxÞÞand the P-upper approximation of x(denoted by PÃðxÞÞare defined as follows:PÃðxÞ¼f y2U:½yU=INDðPÞ#Xg;PÃðxÞ¼f y2U:½YU=INDðPÞ\X–/g:ð4Þwhere PÃðxÞis the set of all objects from U which can certainly be classified as elements of x employing the set of attributes P.PÃðxÞis the set of objects of U which can be classified as elements of X using the set of attributes P.Let P;Q#A,the positive region of clas-sification U=INDðQÞwith respect to the set of attributes P,or in short,P–positive region of Q,is defined as POSðQÞ¼U X2U=INDðQÞPðxÞ: POS PðQÞcontains objects in U that can be classified to one class of the classification U=INDðQÞby attributes P.The dependency of Q on P is defined as:cPðQÞ¼cardðPOS PðQÞÞ=cardðUÞ:ð5ÞAn attribute a is said to be dispensable in P with respect to Q,if cPðQÞ¼k PÀf a gðQÞ;otherwise a is an indispensable attribute in P with respect to Q.Let S¼ðU;A;V;fÞbe a decision table,the set of attributes PðP#CÞis a reduce of attributes C,which satisfies the following conditions:cPðDÞ¼c CðDÞ;c PðDÞ–c P0ðDÞ8P0&P:ð6ÞA reduce of condition attributes C is a subset that can discern decision classes with the same accuracy as C,and none of the attri-butes in the reduced can be eliminated without decreasing its distrainable capability(Pawlak,2002).Obviously,reduction is a feature subset selection process, where the selected feature subset not only retains the representa-tional power,but also has minimal redundancy.So,RST methodol-ogy-based dimensionality reduction will get a good feature subset. Some RST-based reduction and feature selection algorithms have been proposed.Consistency of data(Mi,Wei-Zhi,&Wen-Xiu, 2004;Pawlak,1991),dependency of attributes(Wang,Hu,&Yang, 2002),mutual information(Skowron&Rauszer,1992),discernibil-ity matrix(Jue&Duo-Qian,1998)and genetic algorithm are em-ployed tofind reducts of an information system(Moradi, Grzymala-Busse,&Roberts,1998).And these techniques are ap-plied to text classification(Swiniarski&Hargis,2001),face recog-nition(Liu&Setiono,1998),texture analysis(Swiniarski& Skowron,2003)and process monitoring(Dubois&Prade,1992). An extensive review about RST-based feature selection was given in Thangavel and Pethalakshmi(2009).3.2.Support vector machinesSupport vector machines(SVM)is the theory based on statis-tical learning theory.It realizes the theory of VC dimension(for Vapnik–Chervonenkis dimension)and principle of structural risk minimum(SRM).The whole theory can simply be described as follows:searching an optimal hyper plane satisfies the request of classification,then using a certain algorithm to make the mar-gin of the separation beside the optimal hyper plane maximum while ensuring the accuracy of correct classification.According to the theory,we can classify the separable data into classes effectively.The following is the brief introduction of SVM in cases.Suppose we are given a set of training data x i2R n ði¼1;2;...;nÞwith the desired output y i2þ1;À1f g correspond-ing to the two classes.And suppose there exists a separating hyper plane with the target functions wÁx iþb¼0(w represents the weight vector and b represents the bias).To ensure that all training data can be classified,we must make the margin of separation 2=wk kðÞmaximum.Then,in the case of linear separation,the linear SVM for optimal separating hyper plane has the following optimi-zation problem,Minimize/ðwÞ¼12w T wð7ÞSubject to yiðx iÁwþbÞP1;i¼1;2...;nð8ÞThe solution to above optimization problem can be converted into its dual problem.We can search the nonnegative Lagrange multipliers by solving the following optimization problem, Maximize QðaÞ¼X ni¼1a iÀ12X ni¼1X nj¼1a i a j yiyjx Tix jð9ÞSubject toX ni¼1a i yi¼0a i P0;i¼1;2...;nð10ÞThe corresponding training data are the support vectors.Sup-pose aÃi are the optimal Lagrange multipliers,the optimal weight vectors arewüX ni¼1aÃiyix ið11ÞThe optimal biases arebüy jÀX ni¼1yjaÃix Tix jð12ÞThen,the optimal equation for classification isfðxÞ¼sgn fðwÃÁxÞþbÃgð13ÞC.-C.Yeh et al./Expert Systems with Applications37(2010)1535–15411537The above discussion is restricted to the case that the training data are separable.To generalize the problem to the non-separable case,slack variable e i P0;i¼1;2;...n is introduced under the constraints of(10).The objective equation isMinimize/ðw;eÞ¼12w T wþCX ni¼1e ið14ÞSubject to yiðw T x iþbÞP1Àe i e i P0;i¼1;2;...;nð15ÞC is the nonnegative parameter chosen by users.Solving the problem is similar to the problem of the case of lin-ear separation.But the constraints are changed to beX n i¼1a i yi¼006a i6C;i¼1;2;...;nð16ÞAs to the non-linear separable data,the data can be mappedinto a high dimensional feature space with a nonlinear mapping in which we can search the optimal hyperplane.The linear classi-fication after mapping is performed by selecting the appropriate inner-product kernel that satisfies the Mercer’s condition.Then the problem is converted into searching the nonnegative Lagrange multipliers f a i g n i¼1by solving the following optimization problem (Gold&Sollish,2005;Sinalingam&Pandia,2005;Zhu&Zhang, 2003),Maximize QðaÞ¼X ni¼1a iÀ12X ni¼1X nj¼1a i a j yiyjKðx i;x jÞð17ÞSubject toX ni¼1a i yi¼006a i6C;i¼1;2;...;nð18ÞHence,thefinal classification function isfðxÞ¼sgnX ni¼1aÃiyiKðx i;x jÞþbÃ()ð19ÞThe common used kernel function is RBF kernel function.Kðx;x0Þ¼expÀk x;x0k22r2!ð20ÞFinancial applications of SVM typically focus on pattern match-ing,classification and forecasting.Haärdle,Moro,and Schaäfer (2003)employed SVM to predict bankruptcy and compared with NN,MDA and learning vector quantization(LVQ)(Fan&Palanisw-ami,2000).SVM obtained the best results,followed by NN,fol-lowed by LVQ and followed by MDA.Van Gestel et al.(2003)also reported on the experiment with least squares SVM,a modified version of SVM,and showed significantly better results in business failure prediction when contrasted with the classical techniques.4.Research data and experimentsThe objective of the study is to use efficiency as predictive vari-ables and propose a novel model,RST–SVM,to increase the accu-racy for the prediction of business failure.To test whether efficiency variable will be helpful in business failure predictions, our approach is based on the rationale that withfinancial ratios al-ready been included as independent variables,testing whether the inclusion of DEA will provide extra information about improving the classification accuracy of the prediction model.As we also like to see whether RST can be a good supporting tool in deciding the input variables of the SVM prediction model,the objective of the proposed study is to explore the performance of business failure predictions by proposed RST–SVM model.In thefirst stage,RST is selected for doing variable selection because of its reliability to obtain the significant independent variables.The second stage of the study will use the obtained significant independent variables from RST as inputs of SVM models.The obtained results can then be compared to see whether the one including DEA will give better classification accuracy or not.Finally,for verifying the applicability of methodology,we also designed RST–BPN model as the benchmark.The research data we employ are provided by Taiwan Stock Ex-change(TSE)and database of the Taiwan Economic Journal(TEJ)in Taiwan and consists of the information and electronic manufactur-ingfirms,which arefiled for bankruptcy from2005to2007.The criteria for sampling required that once a company was announced that stocks needed to be‘‘Traded”or‘‘Terminated.”In other words, it may have been cited as(1)having credit crisis,(2)having net operating loss,(3)failing to pay debts,or(4)violating for regula-tion.A failedfirm was paired with a healthyfirm by(1)industry, (2)products,(3)capitalization and(4)values of assets.The size of matched sample was114firms,including38failedfirms and 76healthyfirms.After deleting variables with missing values,the previous research,experiences from past decisions,and the domain knowl-edge offinancial experts in that industry,there are18attributes (including17financial ratios and DEA)and by the binary assign-ment to a decision class(healthy or unhealthy,coded by1and2, respectively).For the DEA,informative input and output variables should be selected.Generally,the input variables for a corpora-tion are capital,liability,human resources,technology,etc.and the output variables are commonly profit and sales.Therefore, in this paper,we selected R&D expense,R&D designers and the number of patents and trademarks as the input variables for DEA,and the output variable included gross profit and market share.To pick out the significant independent variables that are infor-mative and closely related to the corporate condition,in this study, the RST-based application RSES is a collection of algorithms and data structures for rough set computations,developed at the Group of Logic,Inst.of Mathematics,University of Warsaw,Poland.and in particular the genetic algorithm(Komorowski,Øhrn,&Skowron, 2002)were used.The selected variables for this research are shown in Table1,and these eight variables are taken as the input of the classifier of SVM and BPN.5.Results and analysis5.1.Two-stage hybrid model in integrating RST and SVMAfter RST analysis wasfinished and holdout sample was sepa-rated into two groups,we tested whether DEA will be helpful in business failure predictions.Next,hybrid model proposed in this paper is composed of RST and SVM with two groups.In this study, we tested these two possible hybrid models.RST–SVM model only usesfinancial ratios as independent variables which is model I,and RST-SVM model includes bothfinancial ratios and DEA which is model II.Table1Definition of variables.Variables DescriptionX1Working capital/total assetsX2Total debt/total assetsX3Net income/total assetsX4Current assets/total assetsX5Current assets/salesX6Net income/(total assetsÀtotal liabilities) X7Account receivable turnoverX8DEA1538 C.-C.Yeh et al./Expert Systems with Applications37(2010)1535–1541In SVM,we applied the LIBSVM program,downloaded from .tw/wcjlin/libsvm/,to construct the classi-fication model and chose Gaussian RBF as the kernel function. There are two parameters associated with the RBF kernels:C and r.Some kind of parameter-selection procedure has to be done. Hsu,Chang,and Lin(2004)proposed a‘grid search’on C and r and a m-fold cross-validation on the training data.The goal of this procedure is to identify the optimal C and r,so that the classifier can accurately predict unseen data.In m-fold cross-validation,wefirst divide the training set into subsets of equal size.Sequentially one subset is tested using the clas-sifier trained on the remaining(mÀ1)subsets.Thus,each instance of the whole of training set is predicted once,so the cross-validation accuracy is the percentage of data that are correctly classified.The cross-validation procedure can prevent the overfitting problem. In this paper,we performed the5-fold cross-validation to choose the proper parameters of C¼f20;21;...;27g and r¼f2À3;2À2;...;23g.After conducting the grid-search for training data,we found that the results of the confusion matrix using the obtained two hy-brid models can be summarized in Tables2and3respectively. From the results in Tables2and3,we can observe that the average correct classification rate is83.33%for the model only considering financial ratios and86.84%for the model considering bothfinancial ratios and DEA.From the improved correct classification rate of the model considering bothfinancial ratios and DEA,DEA should be helpful in improving the classification accuracy of the prediction model.5.2.Two-stage hybrid model in integrating RST and BPNSince Vellido,Lisboa,and Vaughan(1999)pointed out that around80%of business applications using neural networks will use the BPN training algorithm,for verifying the applicability of SVM,we will also use the popular BPN as the benchmark.As rec-ommended by Cybenko(1989)and Hornik et al.(1989)that the network structure with one hidden layer is sufficient to model any complex system with any desired accuracy,the designed net-work model will have only one hidden layer.In this study,we tested these two possible hybrid models.RST–BPN model only usesfinancial ratios as independent variables which is hybrid model III,and RST–BPN model includes bothfinan-cial ratios and DEA which is hybrid model IV.After comparing the prediction results of the testing sample with different combina-tions of hidden nodes and learning rates,the network structure was7-9-1and8-9-1for input layer,hidden layer and output layer for the model III and IV respectively.We used sigmoid function for activation and Levenberg–Marquardt algorithm for learning.The BPN were executed by MATLAB NN toolbox.The prediction results of the testing sample(the confusion matrix)using the two hybrid prediction models are summarized in Tables4and5respectively.From the results revealed in Tables4and5,we can observe that the average correct classification rate is78.95%for the model only includingfinancial ratios,and82.46%for the model incorporating bothfinancial ratios and DEA.Again from Table6,the improved correct classification rate of the model considering bothfinancial ratios and DEA,we can also conclude that DEA should provide ex-tra information other thanfinancial ratios in improving the classi-fication accuracy of the prediction model.5.3.Results compared with Type I and Type II errors of the constructed modelsIt is well known that,in order to evaluate the overall classifica-tion capability of the designed business failure prediction models,Table2RST–SVM model(model I)classification results with onlyfinancial ratios.Actual class Classified class1(Healthy)2(Unhealthy)1(Healthy)64(84.21%)12(15.79%) 2(Unhealthy)7(18.42%)31(81.58%)Average correct classification rate:83.33%.Table3RST–SVM model(model II)classification results with bothfinancial ratios and DEA. Actual class Classified class1(Healthy)2(Unhealthy)1(Healthy)65(85.53%)11(14.47%) 2(Unhealthy)4(10.53%)34(89.47%)Average correct classification rate:86.84%.Table4RST–BPN model(model III)classification results with onlyfinancial ratios.Actual class Classified class1(Healthy)2(Unhealthy)1(Healthy)63(82.89%)13(17.11%) 2(Unhealthy)11(28.95%)27(71.05%)Average correct classification rate:78.95%.Table5RST–BPN model(model IV)classification results with bothfinancial ratios and DEA. Actual class Classified class1(Healthy)2(Unhealthy)1(Healthy)63(82.89%)13(17.11%) 2(Unhealthy)7(18.42%)31(81.58%)Average correct classification rate:82.46%.Table6Predictive accuracies of the constructed model.Model Accuracy(%)(1-1)(2-2)Average accuracyRST–SVM(model I)84.2181.5884.21RST–SVM(model II)85.5389.4786.84RST–BPN(model III)82.8971.0578.95RST–BPN(mode IV)82.8981.5882.95Table7TypeI and TypeII errors of the constructed model.Model Performance assessment(%)TypeI error TypeII errorRST–SVM(model I)15.7918.42RST–SVM(model II)14.4710.53RST–BPN(model III)17.1128.95RST–BPN(mode IV)17.1118.42C.-C.Yeh et al./Expert Systems with Applications37(2010)1535–15411539。