learning algorithms (with heterogeneous model repre-

sentations) to a single data set, and concluded that to

some degree FDP based on combination of multiple clas-

sifiers was superior to single classifiers according to ac-

curacy rate or stability. Tsai and Wu [22] ensemble mul-

tiple classifiers which were diversified by using neural

networks on different data sets for bankruptcy prediction,

and their experimental results showed that multiple neu-

ral network classifiers did not outperform a single best

neural network classifier, based on which they consi-

dered that the proposed multiple classifiers system may

be not suitable for the binary classification problem as

bankruptcy prediction.

The purpose of this paper is to apply Fuzzy Clustering

Means in going concern prediction model. Fuzzy C-

Means (FCM) clustering is one of well-known unsuper-

vised clustering techniques, which allows one piece of

data belongs to two or more clusters.

The paper is organized as follows. In the next section

we review the Fuzzy C-Means (FCM). The proposed

method is explained in Section 3 with some experiments.

In Section 4 we present our findings. Final section in-

cludes the conclusion .

2. Technical Background

Fuzzy C-Means

FCM theory is the perfect one among many fuzzy clus-

tering analysis methods that are effective for pattern re-

cognition; details can be seen in reference. Considering a

sample set X = {x1, x2, ···, xN}, xi Rs, which is requir-

ed to be divided into C categories; the aim of FCM is to

obtain each category’s clustering centre vc by minimizing

the weighed square sum of inner-cluster error.

Therefore, its objective function is as follows

2

11

,1

CN m

mcncn

cn

JUVd m

,

， (1)

With constraints

1

1

01, 1, 1

0<< ,1,

1, 1

cn

N

cn

n

C

cn

c

cC nN

s.t.Nc C

nN

(2)

where m is the smoothing parameter, which makes it

effective from hard c-means to FCM. This parameter

controls the sharing degree among each fuzzy categories,

bigger m will result in more fuzzy division, or results in

more definitive division. Its experimental range is 1.1 - 5;

μcn is subjection of xn to the cth category; dcn represents

the distance between xn and vc, which often is measured

in Euclidean space. Ji(U, V)—the object ive function

2T

cnncnc nc

dxvxvxv

(3)

U and V can be optimized by performing a number of

Copyright © 2012 SciRes. OJAcct

M. MORADI ET AL.

40

iterative computations using following Equations (4) to

(6), whose astringency has been pro ve d

21

1

ln

1

/

0,

1,

n

m

C

tn cn

c

n

IΦ

dd

cI

cInΦ

(4)

where

|1,01,2, ,

ncnnn

I

ccCd ICI (5)

1

1

1xn

Nm

cc

m

Nn

cn

n

v

n

(6)

3. Research Method

In this section we explain process of data collection and

features selection, then we review fuzzy clustering algo-

rithm.

3.1. Data Collection and Preprocessing

The database used in this study was obtained Iranian

Stock Exchange. Based on the background of Iranian

listed companies, the criteria whether the listed company

is Specially Treated (ST) by Iranian Stock Exchange is

used to categorize financial state into two classes, i.e.

normal and distressed. The most common reason that

Iran listed companies are specially treated by Iranian

Stock Exchange is that they have had accumulated loss to

Stockholders’ equity more than half (Iran Business law

141 Article). ST companies are considered as companies

in financial distress and those never specially treated are

regarded as healthy ones. This experiment uses financial

data two years before the company is specially treated,

which is often denoted as year (t-2) in many literatures.

The data used in this research obtained from Iran

Stock Market and Accounting Research Database. Ac-

cording to the data between 2000 and 2009, 70 pairs of

companies listed in Tehran Stock Exchange are selected

as initial data set. The preprocessing operation to elimi-

nate missing and outlier data is carried out: 1) Sample

companies in case of missing at least one financial ratio

data were eliminated. 2) Sample companies with finan-

cial ratios deviating from the mean value as much as

three times of standard deviation are excluded. After eli-

minating companies with missing and outlier data, the

final number of sample companies is 120.

3.2. Feature Selection

The current study employs 24 variables. The ratios ini-

tially selected allow for a very comprehensive financial

analysis of the firms including financial strength, liquid-

ity, solvability, productivity of labour and capital, vari-

ous kinds of margins and profitability and returns. Al-

though, in the context of linear models, some of these

variables have small discriminatory capabilities for de-

fault prediction, the non-linear approaches used here can

extract relevant information contained in these ratios to

improve the classification accuracy without compromis-

ing generalization. Feature selection is an important issue

in bankruptcy prediction, as in other problems where a

large set of attributes is available, since elimination of

useless features may enhance the accuracy of detection

while reducing the amount of time for processing the

data. Due to the lack of an analytical model, the relative

importance of the input variables can only be estimated

through empirical methods. A complete analysis would

require examination of all possibilities, for ex ample, tak-

ing two variables at a time to analyze their dependence or

correlation, and then taking three at a time, etc. This,

however, is both infeasible and not error free since the

available data may be of poor quality in sampling the full

input space. 24 financial ratios covering profitability,

activity ability, debt ability and growth ability are se-

lected as initial features (see Table 1).

3.3. Designing Fuzzy Clustering Algorithm

One another data mining techniques is fuzzy clustering. In

fuzzy clustering the fuzzy separation is performed that is

each data with one degree of belong is belonged to each

cluster. In actual circum stances Fuzzy clustering is very

more normal than hard clustering because existing data are

not farced fully to depend to one of the clusters in different

clusters border and they are separated with a belong degree

ranging from 0 to 1, indicating their relation belong.

Fuzzy set theory in clustering analysis is focused on

fuzzy clustering based on fuzzy relations and objective

functions.

With regard to provided explanations the fuzzy clus-

tering algorithm is stated as follow (Table 2).

4. Research Findings

Fuzzy clustering algorithm has been designed so that

in the first stage the data are divided to two distinctive

clusters. For this purpose, this technique will determine

effective features that cause to the best clustering. De-

termining effective features is performed by using acci-

dently selection method which it test different fea-

tures1000 times to achieve to the best clustering. This

algorithm is started with determining an effective feature.

On the other hand, this features result in the best cluster-

ng and this trend. i

Copyright © 2012 SciRes. OJAcct

M. MORADI ET AL.

Copyright © 2012 SciRes. OJAcct

41

Table 1. Definition of predictor variables.

Variable Financial Ratios Description VariableFinancial Ratios Description

X1 Funds provided by operations to

stockholders’ equity X13 Accumulated earnings to total assets

X2 Funds provided by operations to total liabilities X14 Current ratio

X3 Net working capital to total assets X15 Interest expenses to total expenses

X4 Total assets turnover X16 Debt ratio

X5 Monetary asset to current assets X17 Inv entory stock turnover

X6 Monetary asset to current liabilities X18 Gross income to sales

X7 Earnings before interest and taxes to

interest expenses X19 Net income to Stockholders’ equity

X8 Net interest expenses to total liabilities X20 Net income to sales

X9 Funds provided by operations

to net working capital X21 Net working capital to sales

X10 Earnings before interest and taxes to total assets X22 Intere st ex pens es to sales

X11 Natural logarithm total assets X23 Interest expenses to net working capital

X12 Inventory stock to curren t assets X24 Market value stockholders’ equity to total assets

Table 2. Fuzzy clustering algorithm.

a) Initial amount is consist of determining the number of clusters, amount of repeat parameter, error maximum, belong functions for one

data on all clusters.

b) k = 1 is clustered by one feature. Fe atures 1 to 24 are aligned randomly.

c) Centers of clusters and covariance matrix are determined by using relevant equivalents.

d) Amounts of data belong degree to clusters are determines according to related equivalents.

e) The repeat from b) to d) as many as 1000 times to reach the objective function to the best local minimum then algorithm is stopped.

f) Selecting effective better k based on the best result of pre-stated crit eria.

g) Increasing k and repeating from second step until k = 24 is obtained.

Summary of research results based on selection feature

have been provided in the following Table 4:

Will continue until to select all of the features for

clustering; summary of results from testing algorithm

based on fuzzy clustering by using data in the year of

occurring financial distress(t year) have been provided in

the following exh ibit (Table 3).

where:

α1: Number of accurately categorized total going con-

cern data/on number of total going concern data.

α2: Number of total accurately categorized financial

insolvent data/number of total fin anc ial insolvent data

The nearer the being different of two clusters is the

better the clustering it is and there is maximum non-

conformity between two clusters. As it is seen between

selecting 3 features to 12 features it have been obtained

identical percents. That is, in this algorithm selection of

two and twelve features for clustering have similar re-

sults and there is not any difference between degrees of

non-conformity between two clusters.

β1: Number of incorrect data in the first group/number

of total incorrect da ta and

β2: Number of incorrect data in the second group/

number of total incorrect data.

As it is observed the feature 7 (Earnings before interest

and taxes to sales) have played an important role in ca-

tegorizing data and it result in better clustering. With

feature 7 the two fuzzy clusters is generated, 93.33 per-

cent (α1) have conformity with going concern group and

100 percen t (α2) have conformity with financial inso lvent

and all errors (β1) is related to going concern cluster.

Now, another test is performed to determine degree of

conformity for each data (firms) by Iran Business Law

Article 141. In this stage, the percent of conformity for

two generated clusters by fuzzy clustering with two clus-

ters that have been categorized to going concern firms

and insolvent groups according to article 141 is tested. It

could be determined their belong percent to each groups. As it is observed the percent of going concern classi-

fication have not been improved as the features increase

M. MORADI ET AL.

42

Table 3. Determining effective features by using fuzzy clustering in the year of financial distress.

Number of item Effective features Degree of non-conformity

1 7 0.9643

12 17, 2, 12, 11, 15, 10, 9, 4, 20, 23, 7, 8 1.000

18 20, 22, 23, 1, 4, 14, 2, 15, 17, 9, 8, 7, 5, 6, 3, 18, 12, 21 0.9298

24 All 0.8966

Table 4. Conformity between fuzzy clusters and clusters of Business Law Article 141 in financial distress year.

6 α1 α2 β1 β2

7 0.9333 1 1 0

17, 2, 12, 11, 15, 10, 9, 4, 20, 23, 7, 8 0.9167 1 1 0

20, 22, 23, 1, 4, 14, 2, 15, 17, 9, 8, 7, 5, 6, 3, 18, 12, 21 0.95 1 1 0

All 0.9667 1 1 0

until number of selection features would arrive to 18

features for clustering which it indicate 95% of data have

classified correctly. Hereafter as the number of features

increase, the percent of classification is improved until

the clustering with all features result in going concern

data classification with 96.67%. Clustering by this data

based on belong percent of each data result in a classifi-

cation type which generate higher conformity by using

Article 141. Belong percent of data indicate amount of

data dependence in the group.

Results from algorithm test based on fuzzy clustering

by using data in the year before financial distress (t-1

year) have provided in the fo llowing Table 5.

Another test was performed to determine the confor-

mity for each data (firms) by Business law Article 141.

In this test the firms are classified to going concern and

insolvent groups. It could be determine their belong per-

cent to each of groups. Summary of research results

based on selection feature have provided in the following

Table 6.

As it is observed the feature 9 (operating cash to

working capital) have played a more important role in

data classification and it resulted in better clustering. So

that as features increase the percent of classification have

not improved but gradually as features increase the clus-

tering have improved until clustering with 15 features

result in to classify going concern da ta with 98.8%.

Results from algorithm lest based on fuzzy clustering

by using data in two years before financial distress (t-2

year) have bee n pr o vi de d in Table 7.

Now we perform another test to determine amount of

conformity between data (firms) by Business Law Article

141. In this test, firms are classified to going concern and

insolvent group. It could be determine their belong per-

cent to each of the group. Summary of research results

based on selection featu re ha v e provided in Table 8.

As it is observed feature 2 (operating cash to total li-

abilities) is the first important feature for classifying data

and it result in better clustering. Results of research indi-

cated that as feature increase the percent of classification

is improved until (as long as) clustering with 15 features

result in the best classification for going concern data

with 96.67%. However, here after as the features increase

and including inefficient features to the model result of

clustering is reduced.

Generally results of algorithm test based on fuzzy clus-

tering indicated that the model in classifying going con-

cern data using data in the year of financial distress, one

year and two years before financial distress 96.67%,

83.44% and 77.34% of going concern firms classify cor-

rectly respectively and in classifying financial insolvent

data this model classify data in the year of financial dis-

tress, one and two years before it 100%, 100% and

98.32% respectively.

Also, in effective features determination test the re-

sults show that in the year of financial distress the fea-

tures based on leverage ratios (Earnings before interest

and tax deduction to interest cost) result in to separate

two classes better than before and the more far from in-

cident year we are the more important role the features

bases on cash flows (operating net cash flows to working

capital or total debt) in clustering tow classes will play.

Geometrical Describe of Belong Percent for Each

Firms to Going Concern and Insolvent Classes

As it was stated the fuzzy clustering method is able to

determine even belong percent of each one of data to

every class so that it is observed this method convey data

(x) is belong to going concer n class with 80% and belon g

Copyright © 2012 SciRes. OJAcct

M. MORADI ET AL. 43

Table 5. Determining effective features by fuzzy clustering in the year before financial distress.

Number of item Effective features Degree of non-conformit y

1 9 0.9231

4 3, 9, 15, 23 0.9608

15 9, 15, 3, 23, 18, 6, 13, 4, 5, 12, 14, 19, 2, 8, 11 0.8519

24 All 0.8519

Table 6. Conformity for fuzzy clusters with clusters generated based on business law article 141 in the year before financial

distress.

Effective features α1 α2 β1 β2

9 0.94 1 1 0

3, 9, 15, 23 0.9273 1 1 0

9, 15, 3, 23, 18, 6, 13, 4, 5, 12, 14, 19, 2, 8, 11 0.9818 1 1 0

All 0.8344 1 1 0

Table 7. Determining effective features by using Fuzzy clustering in two years befor e financial distr ess.

Number of item Effective features degree of non-conformity

1 2 0.9667

4 2, 12, 14, 8 0.9677

15 19, 22, 14, 4, 1, 2, 3, 12, 5, 6, 10, 8, 18, 15, 20 0.8769

24 All 0.7538

Table 8. The results of the study.

Effective features α1 α2 β1 β2

2 0.8387 0.8667 0.55 0.45

2, 12, 14, 8 0.9355 0.95 0.5714 0.4286

19, 22, 14, 4, 1, 2, 3, 12, 5, 6, 10, 8, 18, 15, 20 0.9677 0.90 0.25 0.75

All 0.7734 0.9832 0.96 0.04

to insolvent class with 20% and in some data it is ob-

served that data (z) belong to going concern class with

56% and to insolvent with 44%. Especially this problem

matter in the data basses which data of two classes are

selected based on pair sampling. To better understand of

this problem the belong percents of data is indicated

geometrically on the following graphs in the financial

distress occurrence year. Horizontal axis show the num-

ber of firms and vertical axis show the per cent of belong

for data to its class. Financial distress data are in the right

side and going concern data are in the left side in this

axis. The closer the data in its class to top horizontal ax is

or down are, their percent belong to its class is greater.

As it is observed in the above Graphs 1-4 as features

increase in the year of financial distress the two classes

have separated significantly and with high belong percent

are belong (dependent) to their class.

Belong percent of data in year before financial distress

in the following Graphs 5-8 states that as features in-

crease the separation is performed more desirably and

data show more belong to their class.

Belong percent of data in two years before financial

distress in the following Graphs 9-12 is indicated.

Belong percent of data in two years before financial

distress in the above graphs states that as features in-

crease the separation is performed more desirably and

data show more belong to their class. But should be no-

ticed that the more far from the year of financial distress

we are the harder the separation of two classes it is and use

of more variables result on variables interference so that it

Copyright © 2012 SciRes. OJAcct

M. MORADI ET AL.

44

Graph 1. Belong percent of data with one feature.

Graph 2. Belong percent of data with twelve features.

Graph 3. Belong percent of data with eighteen features.

Graph 4. Belong percent of data with all features.

Graph 5. Belong percent of data with one feature.

Graph 6. Belong percent of data with four fe atures.

Graph 7. Belong percent of data with fifteen features.

Graph 8. Belong percent of data with all features.

Copyright © 2012 SciRes. OJAcct

M. MORADI ET AL. 45

Graph 9. Belong percent of data with one feature.

Graph 10. Belong percent of data with four features.

Graph 11. Belong percent of data with fifteen features.

Graph 12. Belong percent of data with all features.

is observed the use of all variables in two years before

financial distress have resulted in data would belong to a

class with lower belong percent. On the other hand, it

could be concluded that the more far from the year of

financial distress we are some features have not neces-

sary efficiency for classification and use of all variables

would not be correct in the model.

5. Conclusion

Results of algorithm test based on fuzzy clustering indi-

cate that the model would cluster going concern data by

using data in the year of financial distress, one two years

be for financial distress with 96.67%, 85.19% and

77.74% respectively for going concern firms. Also, in

effective features determination test the results show that

in the year of financial distress incident the features

based on profitability (earnings before interest and tax

deduction to interest cost) would resu lt in to separate tow

classes more desirably and the more far from year of

financial distress we are, the features based on cash flows

(operating net cash flow to wo rking capital or total debt)

play more important role in clustering tow classes.

6. Suggestions for Future Researches

To guide students and researches interested to research in

the area of subject of present thesis the following sugges-

tions is provided:

1) Sort the data based on their belong percent in fuzzy

clustering to three or four classes.

2) Use different fuzzy clustering method and deter-

mine belong percent of samples based on different tech-

niques to going concern and insolvent classes.

3) Compare this method with other techniques such as

neural networks method or nearest.

4) Use combination of other variables (different an-

other classes of financial ratios) for designing the model.

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