fuzzy cbr

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Predicting financial activity with evolutionary fuzzycase-based reasoning

Sheng-Tun Li a,*, Hei-Fong Ho a,b

a Institute of Information Management, National Cheng Kung University, Taiwan, ROCb Department of Business Administration, Chang Jung Christian University, Taiwan, ROC

Abstract

Predicting financial activity through examining the short-term liquidity is crucial within todays turbulent financial environment.Firms, governments, and individuals all need an effective methodology based on liquidity information that plays performance deterio-ration warning a priori bankruptcy prediction. In this paper, we propose a hybrid decision model using case-based reasoning augmentedwith genetic algorithms (GAs) and the fuzzy knearest neighbor (fuzzy k-NN) methods for predicting the financial activity rate. GAs areused to determine the optimal or near-optimal weight vector of financial features expressed in linguistic values by the expert. A fuzzyk-NN-based CBR scheme is designed to compute memberships of financial activity rates and to provide a more flexible and practicalmechanism for acquiring, creating, and reusing the experts decision knowledge. An empirical experimentation using 746 publicly tradedTaiwanese firms shows that the average accuracy of the rating is about 92.36%, which is superior to other related models. The proposedapproach not only can lend support to the decision of an expert, but also allow proper feedback for the expert to improve the quality ofthe decision. 2007 Elsevier Ltd. All rights reserved.

Keywords: Case-based reasoning; Genetic algorithms; Fuzzy similarity; Fuzzy nearest neighbor algorithm; Financial activity prediction

1. Introduction

Many financial performance predictions are to assign acorporation to one of pre-determined classes. Such classifi-cation involving the performance and viability of a corpo-ration relies heavily on the information of financialstatement analysis. The fundamental approaches for theanalysis include trend analysis, financial statement com-

parison and financial ratio analysis, etc. Among them,the financial ratios compiled from financial statements wereconsidered to have better measures of a corporate currentperformance than the individual items on the financialstatement (Brigham & Gapenski, 1999) and were widelyaccepted because it could make the message of the financialstatement more attractive. But the representative and the

meaning of the related ratios are always interpreted bythe expert, namely, the financial ratio analysis requiresquite extensive domain expertise. The results of the classi-fication deploying financial ratio analysis are crucial tothe manager because, based on this information, she/hecan realize the present financial status and make the deci-sion for the future plan (Zopounidis, Doumpos, & Matsat-sinis, 1997). And the investor can predict the running

potential and adjust his investment referring to these clas-sification results (Jo & Han, 1996; Kim & Han, 2000;Kryzanowski, Galler, & Wright, 1993; Lee, 2007; Li, Shue,& Shiue, 2000; Oh & Kim, 2007; Yang, Platt, & Platt,1999). Different techniques, ranging from expert analysis(Matsatsinis, Doumpos, & Zopounidis, 1997; Nedovic &Devedzic, 2002; Wagner, Otto, & Chung, 2002) to sophis-ticate decision support systems (Kiang, 2003; Pal & Pal-mer, 2000), have been used to solve the classificationproblem. The most frequently used statistical methods fora classification that involves assignment of an observation

0957-4174/$ - see front matter 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.eswa.2007.09.049

* Corresponding author. Tel.: +886 6 2757575x53126; fax: +886 62362162.

E-mail address: [email protected] (S.-T. Li).

www.elsevier.com/locate/eswa

Available online at www.sciencedirect.com

Expert Systems with Applications 36 (2009) 411422

Expert Systemswith Applications
mailto:[email protected]:[email protected]

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to predefined classes are multiple discriminate analysis(MDA) (Altman, 1968), logistic regression (logit) analysis(Dimitras, Zanakis, & Zopounidis, 1996; Martin, 1997),probit analysis, and ordinary least squares methods (Gess-ner, Malhotra, Kamakura, & Zmijewski, 1988).

While the statistical methods (Tam & Kiang, 1992) have

been used for a long period of time, the artificial intelligent(AI) techniques, recently, become revived to explore theproblems in the commercial applications (Kumar & Ravi,2007; Liao, 2005), such as inductive learning (Han, Chan-dler, & Liang, 1996; Shaw & Gentry, 1998), artificial neuralnetworks (ANNs) (Chun & Kim, 2004; Coakley & Brown,2000; Kim, 2006; Kwon, Han, & Lee, 1997; Lam, 2004; Oh& Kim, 2007; Wong & Selvi, 1998), Rule-Based System(Kim & Lee, 1995; Nedovic & Devedzic, 2002), support vec-tor machines (SVM) (Lee, 2007; Chen & Shih, 2006; Min &Lee, 2005) and Case-Based Reasoning (CBR) (Chiu, 2002;Chun & Park, 2006; Jeng & Liang, 1995; Kim & Han,2001; Oh & Kim, 2007; Shin & Han, 1999). However, CBR

is believed to be a preeminent method for predicting financialactivity by the following reasons. First, CBR is consideredasnon-parametric method which does not require any data dis-tribution assumption for input case. This feature allowsCBR to be applicable to a wider collection of problems thanstatistical techniques such as regression or discriminate anal-ysis. Second, CBR is an incremental learning technique thatcan retain new case without reprocessing to update the pre-vious case base. By contrast, many symbolic manipulationand statistical learning techniques such as decision tree orSVM are batch-oriented, wherein both new and old datamust be submitted as a single batch to the model in order

to generate new mining results. And third, CBR has moreadvantages than ANNs since it not only can process datamore explicitly in explaining analytic results but also canaddress better efficiency in predicting dynamic financialproblem domain (Oh & Kim, 2007).

In spite of the above merits, there are two commonproblems for CBR applications to be solved: one involvesthe determination of the k similar neighbors for the targetcase and another is concerning the weights of attributesspecified in the distance function, which are crucial toCBR effectiveness (Kolodner, 1991). It should be pointedout that the recent argument (Lee, 2007) that CBR doesnot outperform SVM methods is not proper because theauthor did not take fuzzy CBR into account. Fuzzy CBRnot only well performs cross-industrial comparison, butalso provides more friendly suggested solutions, whereinthe fuzzy membership degrees in the solutions can be inter-pretable. This is attractive to the investors.

Therefore, the first objective of this paper is to proposean accurate hybrid decision model for the prediction ofcorporations in financial activity using case-based reason-ing augmented with genetic algorithms (GAs) and the fuzzyk nearest neighbor (fuzzy k-NN) method. GAs are usedto calculate the optimal or near-optimal weight vectorof financial variables whose values are expressed in linguis-

tic terms (fuzzy terms) by the expert. The fuzzy k-NN

algorithm is further to apply weight vector to computethe distances between classes prototypes and input vectors,in which membership in each class is assigned to input vec-tor based on the distance from the prototypes of the clas-ses. The second objective of this paper is to design avisualized hybrid system using aforementioned hybrid deci-

sion model for predicting the financial activity rate fromshort-term solvency indicators and explore the efficiencyof the system in eliciting domain experts knowledge andimparting such knowledge for future decision making. Itwould be highlighted that this investigation has proved thatthe rate of accuracy can be enhanced much higher whenfuzzy set theory was deployed in CBR. This indicates thatthe proposed hybrid system enhances not only learningfrom experience but also the knowledge acquisition, reuseand creation.

The remaining sections of this paper are organized asfollows. Section 2 reviews the relevant literature relatedto the problem. Section 3 presents the hybrid approach

integrating CBR with GA and Fuzzy k-NN. Section 4describes the experimental procedure and depicts experi-mental results and analysis that focuses on the performancecomparisons with other models. In the final section, theconclusions and future work are presented.

2. Literature review

Prediction of Corporation in financial status has drawna lot of attention for more than three decades. Many earlierworks on financial performance classification have focusedon bankruptcy prediction. Beaver (Beaver, 1966) is one of

the pioneer researchers in studying the influence of finan-cial ratios on bankruptcy prediction. Altman (Altman,1968) extended this idea, and proposed the use of MDAbuilt on a set of five financial ratios in bankruptcy predic-tion. While the MDA models have been extensively studiedin the bankruptcy prediction problems for a long time(Blum, 1974; Karels & Prakash, 1987), logit has emergedas another popular technique (Bell, Ribar, & Verchio,1990; Martin, 1997). MDA and logit are parametric tech-niques since they assume certain characteristics of theunderlying data such as normality. By contrast, ANNsand CBR are non-parametric methods because they donot assume the data to have any specific characteristic.These non-parametric based prediction models have beenattractive to researchers for various kinds of problems thatrequire predictions based on financial variables (Arisawa &Watada, 1994; Buta, 1994). Among such problems are loanapplication approval decision (Dietsch & Petey, 2002; Gal-lant, 1988; Li, Shiue, & Huang, 2006; Malhotra & Malho-tra, 2003; Stepanova & Thomas, 2002), prediction ofcorporate bond rating (Dutta & Shekkar, 1988; Shin &Han, 2001), prediction of stock market (Chun & Kim,2004; Jain & Nag, 1995; Kim & Han, 2001; Oh & Kim,2007) as well as the continued studies on bankruptcyprediction (Bryant, 1997; Elhadi, 2000; Gross & Souleles,

2002; Min & Lee, 2005; Park & Han, 2002; Shin, Lee,

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& Kim, 2005). Note that recently, ANNs and CBR havebeen exploited for financial problem domain intensively.Both are classified as non-linear computation method aswell as non-parametric paradigm and share the same meritsat these points. Nevertheless, ANNs have their fair share ofproblems. One common difficulty in neural network appli-

cations is related to the determination of the optimal com-bination of training parameters including the networktopology, the learning rate, the momentum rate, and thetraining methods (Lam, 2004). There are various heuristicrules and common practices for selecting the parameters(Walczak & Cerpa, 1999), but the selection process remainsas an art rather than a science, and varies from problem toproblem. Besides, neural networks are implicit learningtechniques (Chun & Kim, 2004), which comply the non-transparent processes and do not provide any explanationfor users. Oh and Kim (2007) had built DFCI (daily finan-cial condition indicator) with CBR for monitoring Koreanfinancial market and then compared to its counter part

(DFCI with ANNs). They found that the neural networksmay monitor financial market or macroeconomic phenom-ena effectively thank to their over-fitting tendency while thetraining data set is very large. This is not desirable forfinancial studies since modern financial market tends toundergo change of its mechanism over a short period oftime and hence needs to be updated regularly with rela-tively small amount of data. They concluded that CBR ismore sensitive to markets deviation from the stable thanANNs, thus CBR has better efficiency in monitoring finan-cial markets than ANNs (Deboeck, 1994; Kolodner, 1991,1993).

Chun and Kim (2004) explored the implications forportfolio management to obtain superior returns. Theynoted that ANN models suffer from protracted trainingperiods for satisfactory performance in various tasks whileCBR offer much swifter response. The composite approachby coupling implicit learning technique (ANNs) and expli-cit learning (CBR) with active trading strategies had beenbuilt to tackle the primary challenge, which is the determi-nation of the optimal set of weights to construct the com-posite neighbor. They concluded an active strategyinvolving short positions could produce positive returnseven in a bear market. Chun and Park (2006) investigateda relative importance of independent variables from therelationship between independent variables and a depen-dent variable using a regression analysis and put relativeweights using regression coefficients on independent vari-ables for selecting nearest neighbor through the traditionalCBR machine. The investigation against the backdrop of apractical application involving the prediction of a stockmarket index and concluded that regression CBR was sig-nificantly better than standard CBR models in the hit ratemeasure as well as was seen to surpass other models in theMAPLE. Shin and Han (Shin & Han, 1999, 2001) pro-posed the CBR models for corporate bond rating by usinggenetic algorithms and inductive learning. They suggested

to use GAs to find an optimal weight vector for the attri-

butes of cases in case indexing and retrieving. The CBRtechnique provides analogical reasoning structures for pastexperienced cases while GAs provide CBR with knowledgethrough machine learning. Later, they proposed anotherunifying framework to combine general domain knowledgeand case-specific knowledge. The CBR utilizes different

types of knowledge by capturing concrete and specificknowledge related to problem-solving experience, whilethe inductive learning methods provide a general knowl-edge for the application domain, relying on making associ-ations along a generalized relationship between problemdescriptors and conclusions.

In the recent years, CBR has been successfully appliedto the bankruptcy prediction. Elhadi (2000) produced apersonal tool that can assist lawyers in bankruptcy lawand similar fields in doing their law research and reasoningusing previously decided cases to solve new ones. The IR-CBR system they built (BanXupport) try to take advantageof information retrieval and combine with an automatic

indexing IR component in the legal domain of bankruptcylaw. They imitated how lawyers use their mental represen-tations and accumulated experiences in retrieval andunderstanding. And they also used an expert-preparedlaw text as bases for pre-processing and classification inthe IR-CBR system to improve performance. CBR seemsto be more suitable for experience-rich domains. Parkand Han (2002) also confirmed that CBR is an effectivemethod that integrates reasoning methodology and repre-sentation of domain knowledge. They introduced AHPweighted k-nearest neighbor algorithm in assigning relativeimportance in case indexing and retrieving to bankruptcy

prediction for improving classification accuracy. And theresults also provided a basis to integrate qualitative andquantitative criteria, which significantly improves the clas-sification accuracy in the bankruptcy prediction.

For financial performance, the predictive ratios can begrouped under three main categories: profitability, debt,and liquidity and activity (Kryzanowski et al., 1993).Short-term liquidity indicates the activity of the corporateand provides the basis for evaluating the profits andlong-term solvency. The most models have focused onprofitability and debt. To the best of our knowledge, thisinvestigation is the first to study the effectiveness of fuzzyCBR approach for financial performance prediction viaexamining the liquidity and activity of corporations, whichturns to provide earlier observation than bankruptcypredicting.

3. A scheme for evolutionary fuzzy CBR decision model

Lopez de Mantaras and Plaza (1997) pointed out thatthe most severe limitation of all types of existing CBR sys-tems was the feature-value representation that was beingused for cases. They also suggested that the use of Fuzzyset techniques may be more favorable in case representa-tion to allow for imprecise and uncertain values in features

and case retrieval by means of fuzzy matching techniques.

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Basically, CBR performs analogical reasoning while fuzzysets provide the linguistic terms which are suitable for ana-logical representation and reasoning. Moreover, fuzzy logicis effective in eliciting and encoding knowledge fromdomain experts and is well-suited to model continuous,real-world system. Therefore, we apply Fuzzy set tech-

niques to case representation, case indexing and retrievaltogether with evolutionary weight vector in the proposedhybrid decision model in this section.

3.1. Case-based reasoning

A decision system would become more useful as it accu-mulates more experiences. This is especially true in CBRsystem. Leake, Kinley, and Wilson (1997) interpretedhow the CBR could solve the related knowledge in a lim-ited problem domain. Traditional inference mechanismusually draws a conclusion by linking the rules, but CBRapproaches in different ways (Jeng & Liang, 1995; Kolod-

ner, 1993; Shin & Han, 1999). The core of CBR is the casebase which stores a collection of cases from the experiences.If a new problem occurs, CBR recognizes it as a target case,and it would retrieve the most similar k (number of neigh-bors for the source case) relevant exemplar of the targetcase from the case base, use that case to suggest a solutionregarding the new situation, evaluate the proposed solutionand update the system by learning from this experience.Thus, for a given target problem, the problem-solving lifecycle in CBR system essentially consists of the followingfour steps: (see also Fig. 1)

(1) Retrieve: it retrieves one or more relevant cases fromthe memory base.

(2) Reuse: it reuses the information and knowledge in theretrieved cases to solve problems.

(3) Revise: it revises the suggested solution regarding thenew situation.

(4) Retain: it reserving new solution or the experienceonce it has been validated.

Leake et al. (1997) further pointed out that a successfulCBR system could improve main efforts in artificial intelli-gence, namely, knowledge retrieval, knowledge retaining,efficiency of solving the problems, effectiveness of solvingthe cases, and the acceptability of user.

3.2. Fuzzy case-based reasoning

One of the most challenges in CBR system is to computesimilarity between cases. It highly depends on the appropri-ateness and accuracy of the methods used for cases repre-sentation in terms of their corresponding features as wellas the similarity function. Both the initial financial ratioanalysis and the final activity rating require extensivedomain expertise. It is especially difficult for cross-indus-trial quantitative financial market. Most existing investiga-tions use crisp set representation of and traditional distancefunction on matching features, which are time consumingand impractical. Another possibility is to use linguisticterms for expert to narrate his assessments, that is, to turnthe quantitative to qualitative evaluation. It should benoticed that linguistic assessments are not only vague butalso subjective, but if enough data are available, some kindof objective results can be achieved. The proposed fuzzyreasoning model, which comprises case representationmethod for features value using linguistic terms definedas fuzzy sets and an algorithm for analogical reasoningbased on fuzzy theoretic similarity measures, will be dis-cussed in detail.

The linguistic assessments are merely approximate val-ues which are words or phrases in a natural language, like

good or about even, given by the expert (Zadeh,1968). These linguistic assessments are further replacedby suitable fuzzy numbers for arithmetical operations withspecific membership functions like triangular, trapezoidetc. Linear triangular membership functions are consideredto be good enough to capture the vagueness of those lin-guistic assessments, since obtaining more accurate valuesmay be impossible or unnecessary. As Dubois and Prade

Fig. 1. The case-based reasoning cycle (adapted from Aamodt and Plaza, 1994).


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(1980) defined fuzzy sets and their meaning, u~Ax :R ! 0; 1 is the membership function of eA, where eA is aconvex fuzzy set, x is an interested element x 2 R andu~Ax indicates the degree of x in

eA. If the triangularmembership function is considered then there exist exactlyone x0 2 R with u~Ax0 1. The triangular membership

function of eA is expressed as:l~Ax

x l=m l l 6 x < m

u x=u m m 6 x 6 u

0; otherwise

8>: 1

3.2.1. Fuzzy case representation

The universe of each financial liquidity ratio for linguis-tic assessment can be partitioned into n intervals where nfuzzy subsets of the real universe U can be defined. Thatis, for a fuzzy financial activity rating variable eA on Ucan comprise n linguistic assessment terms (fuzzy sets).The membership functions of financial ratio rating can berepresented by u~Axj for a given ratio xj, where xj 2 Xand X is a set of interested corporate financial ratiosX U, eAi 2 eA, i= 1, 2, . . . , n is numbers of linguisticassessment term used.

PiuAixj 1 denotes that the sum

of the membership degrees of all fuzzy assessments at anygiven point is equal to 1. Proposed fuzzy financial activity

rating variable eA comprises five linguistic values from eA1thru eA5eA1 worst; eA2 bad; eA3 even; eA4 better;and

eA5 good; respectively for evaluating financial

liquidity ratio as shown in Fig. 2. The key issue is to judge

the membership functions and interval boundary for eachrating of each financial ratio. The membership functionsand the interval boundaries may fluctuate from time totime. Thus, the judge and the final overall rating requiretremendous mental load. Experienced expert shed the lightto release this burden for approximating these intervalboundaries opportunely. According to Fig. 2, each hori-zontal coordinate gives a maximum of two different mem-bership functions corresponding to two different linguisticratings. For generality, let these membership functions offinancial ratios be represented by

u~Aixj; i 1; 2; . . . ; n; j 1; 2; . . . ;m 2

where i represents the number of linguistic rating terms, jrepresents the number of interested financial ratios (hori-zontal coordinates), respectively. Thus the membership de-gree of each ratio xj of a given case can be obtained by:

Xn

i1

normxju~Aixj; 3

where norm() function will normalize the value of xj intorange [0,1], and the aggregated membership degree of finalrating for a given case can now be obtained by:Xmj1

wjXni1

normxju~Aixj 4

where wj represents the weight of the financial ratio xj, andPmj1wj 1. The weight vector can be obtained from

expert and GA algorithm respectively for comparison pur-pose in proposed system and will discuss more detail innext section.

Concerning computation efficiency and elicitation econ-omy, we transformed the membership degree of financialratios into dominant rating level of financial ratios directlyas follows. If i maximize the u~Aixj then the dominant rat-ing level of the financial ratio xj, expressed as maxu~Aixj,would be equal to i as defined in Eq. (5)

maxu~Aixj i; 5

and the aggregated final rating level of a given case wouldbe as Eq. (6).

Xm

j1

wj maxu~Aixj; 6

Hence, a bipartite vector v

v maxu~Aixj8j;Xmj1

wj max u~Aixj !( )

; 7

is formed for a corporate case, where vector v includesm + 1 elements, first m elements for the dominant ratinglevels of financial ratios in order and the last element forfinal activity rating, i= 1, 2, . . . , n linguistic terms, j= 1,2, . . . , m financial ratios, respectively. Once the case repre-sentation has been decided, we proceed with fuzzy similar-ity measures.

0.5

2 3 4 51

1 2 3 4 5( )jxu ( )jxu ( )jxu

1

0 X

worst bad even better good

( )jxu ( )jxu

Fig. 2. The proposed linguistic assessment terms.


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3.2.2. Fuzzy similarity measures

In fuzzy sets operations, similarity of cases is computedbased on the membership functions of the fuzzy sets asso-ciated to the features of cases. The measuring process heav-ily relates to the real feature format that can be different intypes, such as text, single value, a range, and linguistic

term. Different similarity functions concerning differentfeature types have been proposed, most functions measureupon intersection distance, cosine distance, or Euclideandistance. Euclidean distance notion has used in this paper.Suppose two fuzzy cases vR (retrieved case) and vI (inputcase), and each case vector contains m comparative ratiosx1, x2, . . . , xm and one final activity rating. If Eq. (3) isselected as the membership function of ratios for fuzzycases vR and vI then we adapted Wangs simple and reliablemethod (1997) for case similarity measure as Eq. (8).

simvR; vI Xm

j1

wj 1 Xn

i1

normxRj u~AixRj "

Xni1

normxIju~AixIj

#; 8

For our case consideration, we have transformed themembership degree of financial ratios into dominant ratinglevel of financial ratios as shown in Eq. (5). Therefore weproposed a modified measure to calculate the similaritybetween two fuzzy cases, vR and vI, the formula is

simvR

;vI

Xm

j1 wj

1 1

nmaxu~Aix

Rj maxu~Aix

Ij

;9

where 1 1n

maxu~AixRj maxu~Aix

Ij

is regarded asthe similarity degree of fuzzy set vR and vI on the feature xj,and

Pmj1wj 1 as mentioned above. The sim(v

R, vI) is theweighted average of the similarity degree of fuzzy set vR

and vI, called fuzzy similarity index. The range of sim(vR,vI) is from 0 to 1, which corresponds with the different sim-ilarity degree. sim(vR, vI) = 1 means the two fuzzy sets is

identical; otherwise there exist a difference between twofuzzy sets.

3.3. Feature weighting with GAs

Conventional CBR with the same weight for everyfeature does not reflect the real-world situations, and theprediction ability might be affected as well. So a usefulweight vector for differentiating one case from others iscritical. Many researchers proposed other methods toadjust and improve the feature weightings of CBR andmostly they applied the global search function of GAs to

adjust the feature weights with very good results.

Genetic algorithm was proposed by Holland in 1975(Holland, 1975). The fundamental of this algorithm is toimitate the nature rule of the best survival and obtain anoptimum or nearly optimum solution by learning the his-torical cases. GAs have been widely applied to the fieldsof business, science and engineering. In this investigation,

we propose a hybrid approach using GAs to automaticallyconstruct an optimal or near-optimal weight vector, whichthen compared with weight vector defined by an expert.The reasons for us to adopt GAs to solve feature weightsof problem are as follows.

First, GAs do not need to consider the structure ofproblem. They can start to work by just transforming thespace of the solution to the form of chromosome, whichcould solve the non-linear and restrictive complication ofthe feature weight of distribution. Second, GAs generatemore optimum and feasible solution through the evolutionof chromosome, and the evolution solution of each gener-ation will generate more solutions. Hence they are multi-

point searching methods which can avoid falling into localoptimum solution. Although GAs cannot guarantee thateach evolution solution can get a converged optimum solu-tion, GAs can assist in obtaining the approximate optimumsolution. Third, in searching the space of the solution, GAsare based on the probability rather than the explicit rule sothat it would be more flexible to be applied to the solutionof the optimizing problem.

We apply the classification accuracy rate (CAR) of thetest case set to the fitness function for the proposed system.This fitness function is expressed mathematically asfollows:

max CAR 1

k

Xki1

CAi 10

where

CAi 1 if OTi OSji;

0; otherwise

&;

and

Sji maxsimvR; vI;

For a given i (i= 1, 2, . . . , k) test case, where Sji is themost similar retrieved casej with testing casei (Shin & Han,1999) and O(Ti) is the target output of the test casei. CAi isclassification accuracy for ith test case, denoted by 1 forcorrect, otherwise 0. And CAR is the total classificationaccuracy rate of the test case set. It ranges from 0 to 1.The higher the CAR the closer optimal solution this chro-mosome is. If CAR is equal to one, then classification accu-racy rate is 100% and the corresponding chromosome isoptimal.

3.4. Relevance retrieving with fuzzy k-NN

An effective retrieval of useful prior case plays a central

role in developing a CBR system (Chun & Park, 2006).


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However, the design of an appropriate case matchingprocess in the retrieval step is still in challenging. TheCBR community has proposed several approaches forretrieving particular cases: nearest neighbor, inductive,and knowledge-guided (Barletta, 1991).

Inductive approach is useful when a single case feature is

required as a solution and is more appropriate when thecase is well-defined while nearest neighbor is preferredwhen the retrieval goal is subjective. Inductive indexingrequires large volume of cases and time for maintainingan optimal induction tree (Barletta, 1991; Kolodner,1993). Concerning those factors, we adopt the nearestneighbor retrieval approach for the proposed CBR system.

Nearest neighbor technology provides a simple non-parametric procedure for the assignment of a class labelto the input case bases on the class labels represented bythe closest neighbor of the case. But one of the problemsencountered in using nearest neighbor classifier is that nor-mally each of the sample cases is considered equally impor-

tant in the assignment of the class label to the input case.Another problem is that there is no indication of itsstrength of membership in that class. For problems men-tioned above, we incorporated fuzzy membership into theclassical nearest neighbor similarity function. There aresome advantages of using fuzzy indexing and retrieval.First, fuzzy k-NN defines classes so that a significant reduc-tion in feature space and problem complexity can beachieved. Second, fuzzy k-NN supports the flexibility ofcase matching to allow multiple indexing of a case on fea-tures with different degrees of membership. The inverse dis-tances from the nearest samples to input cases served to

weight the nearest cases class memberships more if theyare closer to the case under consideration. Then the degreeof membership of input case in each class can be specifiedrather than just the crisp result. It should be noted that acases memberships in the resulting classes must sum to

one. Analogous fuzzy nearest prototype algorithm (Keller,Gray, & Givens, 1985) has adopted in the proposed systemfor not only the computational simplicity but also thedesirable membership assignments. The fuzzy nearest pro-totype algorithm listed in Fig. 3.

3.5. Hybrid model with evolutionary fuzzy CBR

A scheme for building hybrid CBR prediction model isillustrated in Fig. 4. In first phase, the features valuesand the final rating of each historical case are convertedinto linguistic values by expert. Then the historical casebase is divided into training set and testing set. GA is thenemployed to generate an optimal or near-optimal weightvector with training set for which the classification out-come has been determined. The chromosomes representas weight vectors for further fuzzy k-NN measuring. Weset the range of the weights between 0 and 1. The fitnessfunction is defined to find the maximum total sum of clas-

sification accuracy ratio of the training set as mentionedabove. The crossover and mutation rates are changed toprevent the output from falling into the local optima.The crossover rate ranges 0.50.8 and the mutation rateranges 0.010.1 in the system. Each solution (weight ofcase) calculates the CAR using 10-fold cross validation.

In second phase, we apply the derived weight vector intofuzzy k-NN matching function to retrieve useful cases fortarget case and the degree of membership of target casein each class can be specified rather than just the crispresult. Finally, the statistic average of accuracy rate andvariation will be computed with additional validation cases

for which the outcome is also known. These processes aredone by the add-in modules called from Mat Lab. As thevalidation cases are not used for optimization process,the prediction performance tested by these cases wouldtend to be objective and effective.

Fig. 3. Fuzzy k-NN prototype algorithm.


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4. Experiment design and analysis

4.1. Experimental design

Step (1) Establishment of the historical case baseFinancial statement analysis requires specific knowledgeand the accumulated experience. Therefore in thisresearch, we had an expert to help us. This selectedexpert was a 40-year-old accountant with seventeenyears working experience related to financial statementanalysis. After discussing with the expert, we selectedsix main indexes as short-term liquidity indicators forpredicting the corporate financial activity. These six fea-tures are illustrated in Table 1.After determining the financial features, the expert des-ignated the importance level of each feature which willbe validated with weight vector found by GAs later.Then he confirmed the corresponding linguistic assess-

ment values and the interval boundaries to the basis ofeach performance level for each feature. These five levelsof linguistic assessment values are worst, bad, even, bet-ter, and good. The expert analyzed available data of 746publicly traded Taiwanese corporations for establishingthe historical case base.Step (2) Evaluation of the financial activityAn example of assigned historical case is shown in Table2. As the expert interviewing the difference of currentratios in the selected case, he explained that current ratiowas decreased by 2.78 which signaled the activity declin-ing. Moreover, AR, INV, and NOC were expected to beas smaller as possible, but the selected case didnt per-form well in the industry at that period. At last, theamount of sales and the operation income had shrunkeven worse. After assigning the proper linguistic assess-ment for each feature, the final financial activity ratingof the selected corporation was assigned to the worstby the expert was shown. The proposed hybrid CBR sys-tem was used to elicit the expertise in linguistic assess-ment terms and to justify experts rating as systemfeedbacks later on.Step (3) Measurement of the importances of the featuresWhen fuzzy CBR was proceeding during the experi-ment, the most important work is to find the accurate

weight values of classification in cases and apply it tothe CBR, namely, this is the measurement of the impor-tances of the features. The simplest way is to inviteexpert to set up these values according to his profes-sional knowledge and experience, but when the experttries to quantify the importance of the decision, usually

Case fuzzification

Training cases

Testing cases

Genetic

Algorithms

Cross-validation

New Problem

Case fuzzification

Case Indexing with similarity

Case retrieval with Fuzzy-kNN

Solution with fuzzy

membership degree

An optimal or

near optimal

weight vector

Domain expert

Historical cases

Fig. 4. A framework for evolutionary fuzzy case-based reasoning.

Table 1Liquidity indicators

CR Current ratioAR Collection period for account receivableINV Days to sell inventoryNOC Net operation cycle

S SalesOI Operation income

Table 2A case evaluated by the expert

2004 2005 Difference Judgment

CR 54.00 51.22 2.78 WorstAR 38.80 40.94 2.14 EvenINV 60.93 75.64 14.71 BadNOC 78.00 80.33 2.33 BetterS 34482535.00 28886355.00 5596180.00 WorstOI 10.54 0.27 10.27 Bad

FINAL RATE Worst

Table 3The weight vector set by the expert

Attributes CR NOC S OI AR INV

Weight values 1 0.8 0.7 0.4 0.2 0.2Accuracy rate 82.50%


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there would be somewhat vague and it cannot be welldefined. Therefore, the experiment of this research wasdivided into two separated procedures: one is to invitethe expert to setup the weight values of attributes, theother is to have GA found the weight vector of the opti-mal or near-optimal. Finally, the results would beexplored to see if the weight values found by GA couldbe consistent with those values made by the expert.First, we explained the manipulation of CBR to expert,and invited the expert to give the weight values of theimportance of each ratio: the most important weightvalue is 1 and the least value is 0 according to his profes-

sional knowledge and experience. Table 3 shows theweight vector set by the expert and the experimentalresult in accuracy rate.Thereafter, we began to proceed the second-part exper-iment of Fuzzy CBR. GA was used to adjust the weightof each ratio. The values of six financial ratios were setfrom 0 to 1, (precision setting is three digits after thedecimal) which reflected the importance of each ratio.Each solution was called a chromosome, which wascomposed of six genes and each gene included seven bitsin the form of a binary string as shown in Table 4. Theroulette wheel selection was used in the research, and the

higher the fitness value, the higher the pick-out proba-bility was. Two-point crossover and single-point muta-tion were adopted in this research. The crossover ratewas set to 0.8 and the mutation rate was set to 0.01.We adopted 10-fold cross validation and divided 746cases into ten equal-sized parts (n1, n2, . . . , n10) arbi-trarily. First, we took n1 as the test cases, and the restnine parts as the training cases. The purpose of the train-ing cases was to get a set of nearly optimized weightvalues which further validated the accuracy of the testcase n1. Then, n2 was taken as the test cases, and the oth-ers as the training cases. Analogously, after proceedingten times, there would be ten sets of the near-optimalweight values and the corresponding accuracy rates asshown in Table 5. Finally, we took the most accurateweight values of these ten sets as the most optimumsolution of the cross validation as shown in Table 6.The experimental results show that the average valueof 10-fold cross validation was 92.36% and the variancewas 13.17.Step (4) Computation of the similarity degreeIn this research, each case was composed of six ratios.We compared six ratios with the corresponding ratiosof input case and calculated similarity degrees betweenratios. Then final similarity values of cases can be

obtained via the matching function. This study adopted

the Euclidean Distance formula in the similarity mea-surement algorithm which was depicted in Eq. (9).

Fig. 5 shows the main menu of the system. The up-leftcorner is the setup domain of the parameters, in whichthe parameters of membership function can be selectedand the weight values of the cases can be set up. The righthand is a function section where the types of the member-ship function of attributes, similarity function of case, andthe adoption of the suggested weighting values of the gainmodule can be selected. The down-left corner shows themembership degree of each solution cases where the expert

can examine the various suggested solutions and makedecision.

4.2. Experimental results and analysis

1. Classification accuracy rate (CAR)In this investigation, the algorithms used in the systemand the empirical results are shown in Table 7, whichshows that the accuracy rate is the worst for the tradi-tional CBR but the best for the proposed Fuzzy CBRwith GA weighted algorithm.

2. Precision and recall

Precision and recall are used to compare the resultingprediction with pre-specified class labels. The precisionfunction evaluates the numbers of the relevant casesretrieved over the numbers of the retrieved cases. The

Table 4The structure of chromosomes

0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1

Gene1 Gene2 Gene3 Gene4 Gene5 Gene6

CR = 0.01 AR = 0.03 INV = 0.07 NOC = 0.15 S = 0.31 OI = 0.63

Table 5The weight vector solutions using 10-fold GA Fuzzy CBR

CR NOC S OI AR INV Accuracy rate

1 0.576 0.293 0.293 0.01 0.01 920.576 1 0.293 0.576 0.01 0.01 89.1890.859 0.434 0.151 0.151 0.01 0.01 921 0.717 0.293 0.151 0.01 0.01 95.946

1 0.859 0.293 0.151 0.01 0.01 93.3331 0.293 0.576 0.434 0.151 0.01 86.6670.859 0.293 0.576 0.293 0.01 0.717 89.1891 1 0.151 0.434 0.01 0.576 90.6671 0.859 0.01 0.01 0.01 0.01 97.2971 0.576 0.293 0.151 0.01 0.151 97.333

Table 6The optimum solution using GA Fuzzy CBR

Attributes CR NOC S OI AR INV

Weight values 1 0.57 0.29 0.15 0.01 0.15

Accuracy rate 97.33%


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recall function evaluates the numbers of the relevantcases retrieved over the numbers of the relevant cases.The formal definitions of precision and recall are:

pi jci \xij

jcijand Ri

jci \xij

jxij11

Or can be expressed also as follows:

P

Xk

i1

jxij

TPi and R

Xk

i1

jxij

TRi 12

where ci is the cases retrieved for the ith case, xi is thepre-specified classification label, and 1 6 i6 T, whereT is the number of cases. (T is 746 herein.) Precisionand recall of classification is defined as above and Table8 depicts the classification results of applying GA, fuzzyk-NN to the financial data sets and the comparison ofthe analyzing difference by GA Fuzzy CBR and expert.Table 9 lists the precision of each 10-fold cross-valida-tion as well as the recall in this study.

When the expert resolves the problems of performanceranking, there is the presence of some vagueness. However,the results of the decision could be accepted only if its dif-ference is restricted in one order, which would lead investornot to make a wrong judgment.

In comparing the related reports in the literature, theaverage error rate of the results is 7% (55/746) as show inTable 8, which is quite low. Thus, the results producedby the add-in module proposed in this investigation havebeen proved to be better. Concerning the inconsistent withclassified results between system and expert, we present thecases with wrong judgment and their original data togetherto the expert for revising the original judgment, which inturn not only would lend support for the GA CBR system

to have more accurate judgment but also can provide the

expert proper feedback, namely, the expert can refine his

decision strategy.

Fig. 5. Evolutionary Fuzzy CBR system.

Table 7Accuracy rate of classification in CBR

The method that parameter set up CAR (%)

Traditional CBR 75.64CBR weighted by expert (proposed) 82.50CBR with AHP weighted k-NN (Park & Han, 2002) 83.00CBR with GA weighted (Shin & Han, 1999) 90.61CBR with weighted k-NN (Yip, 2004) 90.90Fuzzy CBR with GA weighted (proposed) 92.36

Table 8

Predictions between GA Fuzzy CBR and expert

1 2 3 4 5 Total

1 184 9 1 0 0 1942 13 114 10 1 0 1383 0 5 204 4 0 2134 0 0 7 130 3 1405 0 0 0 4 57 61

Total 197 128 222 139 60 746

Table 9Precision & recall for the ten folds

Ten-fold Precision (%) Recall (%)

1 92 922 89 893 92 924 96 965 93 936 89 877 91 898 97 919 97 9710 97 97

Total 92 92


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5. Conclusions and future work

By using fuzzy case representation, the proposed hybridsystem not only provided a more flexible mechanism forcollecting experts knowledge, but also was effective toenhance the accuracy rate of classification. The latter was

indeed supported by the result showing the rate has beenincreased up to 92.36%. In the aspect of the decision ofthe practice, if the first and the secondary fuzzy member-ship degrees are selected in the hypothesis for trend judg-ment, the total accuracy could be further increased to98%, which is very practical for managers and investors.Moreover, the decision model for the automated short-term liquidity performance prediction using Fuzzy case-based reasoning approach not only can lend support tothe decision of an expert, but also allow proper feedbackfor expert to improve the quality of the decision.

There are some limitations in this study. The financialratios selected herein by an experienced expert mainly

showing the way of knowledge elicitation. But the moresophisticated features selection algorithms be applied themore thoughtful prediction could be. Considering the moresophisticated features selection algorithms, this mayinvolve with group decision making. Multiple experts couldbe further invited to contribute their knowledge for maturedecision.

Acknowledgement

The authors would like to thank the experiment workmade by Stella Shao.

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