Applying Rough Sets Theory to Corporate Credit
Ratings
Tien-Chin Wang, Ying-Hsiu Chen

Abstract—Risk assessment and credit rating are
primary criteria to investigate the repayment ability of
borrower for financial institution. The amount of
corporate bond has increased rapidly in recent years.
Bond market in Taiwan has also developed actively.
Bond market is thus an indispensable risk index for
developing the credit rating mechanism. This study
utilizes the rough sets theory and the financial ratios of
credit evaluation of TCRI as criteria. Using the
semiconductor industry of Taiwan stock market as
models, this research finds out several important
reference factors that sway enterprise credit rating. The
credit rating evaluating criteria are grouped into the
following three kinds: good, probably good, probably
bad. Results of this study show that the interest expense
ratio, debt ratio, receives months, sale months play
important roles for overall assessment of enterprises.
Index Terms—Corporate Credit Ratings, Rough Sets,
Taiwan Corporate Credit Risk Index (TCRI).
I. INTRODUCTION
Risk assessment and credit rating are primary criteria for
investigating the repayment ability of a borrower to a
financial institution. The amount of corporate bonds has
increased rapidly in recent years. The bond market in Taiwan
has also developed actively, but the corporate credit line of a
company is often higher.
When a customer breaks a contract, the loss is also serious.
Therefore, the bank must incorporate better risk management
to maintain its corporate credit line and lower the risk of
financial loss incurred through broken contracts. The bond
market is thus an indispensable risk index for developing the
credit rating mechanism.
At present, the most pervasive way of analyze of bank
credit is the “5P” principle, a factor of borrowed money
(People), fund use factor (Purpose), refund source factor
(Payment), the creditor's rights guarantee (Protection), and
Tien-Chin Wang, corresponding author, Professor, Department of
Information Management, I-Shou University, 1, Section 1, Hsueh-Cheng
Road, Ta-Hsu Hsiang, Kaohsiung County, Taiwan 840. (phone:
+886-7-6577711
ext
6568;
fax:
+886-7-6577056;
e-mail:
tcwang@isu.edu.tw ).
Ying-Hsiu Chen, Doctoral Student, Department of Information
Engineering, I-Shou University (e-mail: yingshow@ms28.hinet.net).
factor of vision of the future (Perspective). An alternative is
using the “5C” principle as the standard of credit rating,
which is character, capital, capacity, collateral and condition.
Its purpose and appraisal essential factor has the same stead
with the 5P principle.
Credit ratings of enterprises are vague and uncertain.
Therefore, this study utilizes the rough sets theory (RST)
proceeds to in corporate credit rating. RST represents a
different mathematical approach to vague and uncertain data.
Using the semiconductor industry of the Taiwan stock market
as a model, the attribute result of the Taiwan Corporate
Credit Risk Index (TCRI) is used to analyze and extract the
important factors that influence enterprise credit ratings.
Classify the credit rating results and determine which
enterprises belong to low risk and claim investments. The
findings in the research will be the reference materials of the
bank in their credit rating decision.
II. LITERATURE REVIEW
This study utilizes the rough sets theory to analyze the
attributes of corporate credit ratings. In literature review,
section 2.1, 2.2 and 2.3 discuss the meaning of credit ratings,
related criteria of research and empirical application result.
Section 2.4 focuses on the applications of rough sets.
2.1. Credit Ratings
Credit rating is an estimate of credit condition or the ability
to pay debt. Financial institution follows the certain
procedure, using the statistical method to lay down a number
of rating standards which accesses an enterprise’s credit
situation and gives an overall default risk assessment. Getting
each credit attribute gives the quantification, and calculates
its points and rating. According to the rating the quality of
credit is decided [1], [2]. In addition, when this credit
intensity changes, a financial institution can promptly make
the suitable revision to the credit rank, to reflect as present
the credit quality.
2.2. The related criterion of corporate credit ratings
The credit-rating system, currently operated for mid- and
small- scaled business units in Taiwan, consists of three main
categories: Financial Conditions (FC), General Management
(GM), as well as Characters and Perspectives (CP). Credit
rating has been implemented for several years in foreign
countries, however, the mechanism of credit rating in Taiwan
is limited to Taiwan Ratings Corporation and TEJ (Taiwan
Economic Journal Co. Ltd.) to establish more complete
databases.
Taiwan Ratings Corporation encompasses two basic
components its corporate rating methodology: business risk
analysis and financial risk analysis. Each corporate rating
analysis begins with an assessment of the company's
environment. Factors assessed include industry prospects for
growth, stability, or decline, and the pattern of business
cycles. Financial risk is portrayed largely through
quantitative means, particularly by using financial ratios.
Analytical adjustments are made to better portray reality.
TCRI (Taiwan Corporate Credit Risk Index) is a corporate
credit rating system, which was developed by TEJ. The main
risk assessment factors include: profitability, security,
activity and scale. Each factor has several representative
financial ratios. TCRI assesses risk by first obtaining basic
rank by the financial material that estimates a basic synthesis
score by 10 financial values and the ratio (Table 1), then
determines a preliminary basic rank. The next rating depends
on the risk and the scale obtains the threshold rank which is,
finally decided by TCRI using the non-quantification factor.
TABLE 1
TAIWAN CORPORATE CREDIT RISK INDEX
Risk Assessment Factor
Representative Financial ratio
Profitability
Return on Equity (ROE)
Operating Profit (OP)
Return on Asset (ROA)
Security
quick ratio
interest expense ratio
debt ratio
Activity
receives months
sale months
Scale
operating income
total assets
Formula: ROE = recurring income discounted / average
net value; OP = operating revenue / operating income; ROA
= EBIT /average asset; quick ratio = quick asset /current
liabilities; interest expense ratio = interest expense /
operating income; debt ratio = total debt / shareholders'
equity; receives months = 12/(operating income/average
tab); sale months = 12/(cost of operating /average inventory).
Taiwan Ratings Corporation concentrates primarily on the
financial negotiable securities industry due to the general
industry lacking sufficient credit ratings. In addition, TEJ
develops the TCRI implementation by using public
information appraise the credit risk. The information is
obtained conveniently; furthermore TCRI aids this study by
applying rough sets theory to corporate credit rating. Based
on above reason this study adopt TCRI as the evaluate
criteria.
2.3. Empirical application result of corporate credit rating
The bank must have better risk management policies for
assessing to corporate credit lines, in order to lower the risk
that the bank takes on loans. Zimmermann and Zysno [3]
consider that there are many fuzzy characteristics in the
decision-making process, thus, they proposed the use of
fuzzy method expression evaluate criteria. Su and Tsai [4]
combine the traditional finance condition and the fuzzy set
theory, relying on the triangle membership function and
standard fuzzy rating value to establish a ranking. Chen and
Chiou [5] proposed using the fuzzy integral, a fuzzy
approach for rating business credit for commercial loans. The
proposed approach uses fuzzy sets (fuzzy numbers) to
describe the criteria so that the final credit-rating results can
reveal the changes in credit information.
2.4. Application of Rough Sets
The rough set theory has proved to be very useful in
practice, as is clear from the record of many previous real-life
applications. RST may solve the general basic problem, for
example, to make the attribute simplification, to find the
hidden data pattern, as well as account for the
decision-making rule [6], [7].
In particular, the rough sets approach has found interesting
applications in medicine [8], pharmacology, business,
banking, market research [9], engineering design,
meteorology, vibration analysis, switching function, conflict
analysis, image processing, voice recognition, concurrent
system analysis, decision analysis, character recognition, and
other fields [10].
III. ROUGH SET THEORY (RST)
The rough sets theory was proposed by Pawlak in 1982 [6]
to deal with uncertain and fuzzy materials and to simplify
knowledge. In the rough sets theory, humans use their general
knowledge to classify the world around them as abstract or
concrete. Everything is classified according to its
characteristics, and those with nearly identical characteristics
may be put into the same group. This is called indiscernible
relation, denoted as Ind and is the basis of rough sets theory.
One of the main advantages of rough set theory is that it
does not need any preliminary or additional information
about data. The main problems that can be approached using
rough sets theory include data reduction, discovery of data
dependencies, estimation of data significance, generation of
decision algorithms from data, approximate classification of
data, discovery of patterns in data and discovery of
cause-effect relationships [10]. The following is the concept
of rough sets theory [11], [12].
3.1. Information Systems
Knowledge can be finished by the information systems, the
basic composition of an information system is the set of
objects which are to be studied. The knowledge of these
objects is described by their attributes and attribute values.
The information system is defined as follows:
(1)
IS  (U , A)
where U is the universe, a finite non-empty set of objects,
U  {x1 , x2 ,..., xm } , and A is the set of attributes. Each
attribute a  A (attribute a belonging to the considered set
of attributes A) defines an information function:
(2)
f a : U  Va
where Va is the set of values of a , called the domain of
attribute a . In all attributes, there are decision attributes and
condition attributes.
3.2. Indiscernible relation
For every set of attributes B  A , an indiscernible
relation Ind(B) is defined in the following way: two objects,
xi and x j , are indiscernible by the set of attributes B in A, if
b( xi )  b( x j ) for every b  B . The equivalence class of
Ind(B) is called the elementary set in B because it represents
the smallest discernible groups of objects. For any element
xi of A, the equivalence class of xi in relation Ind(B) is
represented as [ xi ] Ind ( B ) .
3.3. Upper and Lower approximations
The rough sets approach to data analysis hinges on two
basic concepts, namely the lower and the upper
approximations of a set, referring to: the elements that
doubtlessly belong to the set, and the elements that possibly
belong to the set. The definition is shown as follows:
Let X denote the subset of elements of the universe U, the
lower approximation of X in B, denoted as BX , is defined as
the union of all these elementary sets which are contained in
X. More formally:
BX  {xi  U xi Ind ( B )  X }
(3)
The above statement is to be read as: the lower
approximation of the set X is a set of objects xi , which
belong to the elementary sets contained in X (in the space B),
BX is called the lower approximation of the set X in B.
The upper approximation of the set X, denoted as BX , is
the union of these elementary sets, which have a non-empty
intersection with X:
BX  {xi U xi Ind ( B )  X  0}
(4)
The above statement is to be read as: the upper
approximation of the set X is a set of objects xi , which
belong to the elementary sets that have a non-empty
intersection with X, BX is called the upper approximation of
the set X in B.
The difference is called a boundary of X in U.
BNX  BX  BX
(5)
3.4. Core and reduct of attributes
The concepts of core and reduct are two very important
concepts of the rough sets theory. If the set of attributes is
dependent, one can be interested in finding all possible
minimal subsets of attributes. These lead to the same number
of elementary sets as the whole set of attributes (reducts) in
finding the set of all indispensable attributes (core).
Simplification of the information system can be used to
recognize some values of attributes which are not necessary
for the system. For example, some attributes which are
redundant can be deleted or be filtered by means of the
simplification procedures. If, Ind ( A)  Ind ( A  ai ) , then
the attribute a i is dispensable, otherwise, a i is indispensable
in A. In other words, if after deleting the attribute a i , the
number of elementary sets in the information system is the
same, then it concludes that attribute a i is dispensable.
Hence, the simplification can contain the minimal subsets
of independent attributes, which ensure they can represent
the whole set. The core is the necessary element for
representing knowledge or rules, and is the common part of
all reducts. The researcher uses the discernibility matrix to
compute the values of reducts and core.
IV. CASE STUDY
Risk assessment and credit rating are primary criteria to
investigate the repayment ability of the borrower to the
financial institution. However, credit rating of an enterprise is
vague and uncertain. Therefore, a researcher can utilize the
characteristic of RST to deal with vague and imprecise data,
and proceed to analysis of corporate credit rating.
This study utilizes the financial ratios of credit evaluation
of TCRI as criteria. Using the semiconductor industry of the
Taiwan stock market as a model, this research discovers
several important reference factors that sway enterprise
credit rating. This research classifies the credit rating results,
and determines which enterprise really belongs to low risk
and claim investment. The findings in the research will be the
reference materials of the bank in their credit rating decision.
4.1. Subjects
This study takes 16 listed companies in the Semiconductor
Industry of Taiwan as research subjects, which are used to
calculate corporate credit rating including: United
Microelectronics
Corp.,
Advanced
Semiconductor
Engineering, Inc., Siliconware Precision Ind. Co., Ltd.,
Orient
Semiconductor
Electronics
Ltd.,
Taiwan
Semiconductor Manufacturing Company, Ltd., Macronix
International Co., Ltd., Mosel Vitelic Inc., Winbond
Electronics Corp., Silicon Integrated Systems Corp., VIA
Technologies, Inc., Sunplus Technology Co., Ltd., Nanya
Technology Corp., Weltrend Semiconductor, Inc., King
Yuan Electronics Co., Ltd., Mediatek Incorporation,
Novatek Microelectronics Corp.,etc.
4.2. The Data
This research takes 11 financial ratios of enterprise credit
risk assessment of TEJ as criteria. The attributes are Return
on Equity (ROE) ( a1 ), Operating Profit (OP) ( a2 ), Return on
Asset (ROA) ( a3 ), quick ratio ( a 4 ), interest expense ratio
( a5 ), debt ratio ( a6 ), receives months ( a7 ), sale months
( a8 ), operating income ( a9 ), total assets ( a10 ), all of the ten
attributes belong to the condition attribute. Another attribute
is TCRI ( a11 ) which belongs to the decision attribute.
this paper. Using the terminology of the rough sets theory,
this data set can be considered as an information
system IS  (U , A) , where universe U and attributes A
correspond to the set of objects and to the set of variables,
respectively:
U  {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16}
A  {a1 , a2 , a3, a4 , a5 , a6 , a7 , a8 , a9 , a10 , a11} , there are 10
The application starts with an appropriate discretization of
the information system by translating the values of the
quantitative
attributes
{a1 , a 2 , a3, a 4 , a5 , a 6 , a 7 , a8 , a9 , a10 , a11 } and of the decision
condition attributes and one decision attribute { a11 }.
attribute { a11 } into qualitative terms (Table 2). The
condition attributes and decision attribute are coded into
three qualitative terms, such as: good, medium and bad. The
results of this evaluation are show as Table 2, where G, M,
and B denote “Good”, “Medium”, and “Bad”, respectively.
This study checks the attributes B  A ( B  {a1 ,..., a10 } ),
if the TRCI of the enterprises are “Good”, this represents that
the enterprise keep the better ability of repayment. According
to Table 2, the enterprises 1, 2, 3, 5, 11, 15 and 16 are
“Good”, we denote the set as X  {1,2,3,5,11,15,16} . We
TABLE 2
THE RESULTS OF THREE MEASUREMENTS PERFORMED FOR 16 OBJECTS
F
a1 a2 a3 a 4 a5 a6 a7 a8 a9 a10 a11
E
1
B
B
B
B
G
G
G
G
B
G
G
2
B
B
B
B
G
G
G
M
B
B
G
3
B
B
B
B
G
G
G
M
B
B
G
4
G
M
M
B
G
B
G
M
B
B
B
5
B
M
M
M
G
G
M
M
G
G
G
6
M
G
M
B
G
M
G
B
B
B
M
7
G
M
G
B
G
G
B
M
B
B
B
8
B
B
B
B
G
G
M
M
B
B
M
9
B
B
B
B
M
G
M
M
B
B
M
10
B
B
M
B
G
G
G
B
B
B
M
11
B
B
B
B
G
M
G
M
B
B
G
12
B
B
B
B
B
G
G
B
B
B
M
13
B
B
B
G
G
M
B
G
B
B
M
14
B
B
B
B
G
G
M
B
B
B
M
15
G
G
G
M
G
M
M
G
B
B
G
16
G
B
M
B
G
G
G
G
B
B
G
F: financial rate; E: enterprise
4.3. Analysis and results
Sixteen enterprises with eleven attributes are evaluates in
The information function f a for this system is presented
in Table 2. The domains of the particular attributes are:
V1 ~ V8 ,V11  {Good , Medium, Bad} V9 ,V10  {Good , Bad}
combine the enterprises which have the same evaluation
results in the attribute B. The results are shown that there are
fifteen elementary sets.
Using Equation (3), the lower approximation of X is
BX  {2,3} , which represent enterprises 2, 3 that certainly
belong to the set of “Good” corporate rating. Using Equation
(4), the upper approximation of X is BX  {1,2,3,5,11,15,16} ,
which represent enterprises 1, 2, 3, 5, 11, 15, 16, and could
belong to the set of “Good” corporate rating. Using Equation
(5), the boundary of X is BNX  {1,5,11,15,16} , which
represents enterprises 1, 5, 11, 15, 16, of uncertain
membership to the set of “Good” corporate rating.
Concerning the core and reduct attributes, we consider the
subsets of A and compute the numbers of elementary sets.
Finding that {a3 , a5 , a6 a7 , a8 } and {a5 , a6 , a7 , a8 , a10 } have
the same number of elementary sets as B, and are minimal
subsets of B we conclude that the two subsets are the reduct
of B.
The core of B, defined by {a3 , a5 , a6 a7 , a8 } 
{a5 , a6 , a7 , a8 , a10 } , are {a5 , a6 , a7 , a8 } , the four attributes
a5 , a6 , a7 , a8 , which have great influence on overall
assessments.
This study according to the decision attribute find that the
overall assessments is a good enterprise as the first step, then
using RST as further analysis, therefore, the same enterprise
will not appear in this study but obtain a different credit
rating.
V. CONCLUSIONS
Risk assessment and credit rating are primary criteria used
to investigate the repayment ability of a borrower to a
financial institution. The bank must have better risk
management ability to access corporate credit lines, in order
to lower the risk that the bank makes on loans. Because of the
credit rating of an enterprise is vague and uncertain. This
study applies another analysis method─rough sets theory
(RST) ─ to determine the corporate credit ratings. The
purpose of this study is to utilize the characteristics of RST to
deal with vague and imprecise data, which is used corporate
credit rating.
This study utilizes the financial ratios of credit evaluation
of TCRI as criteria. Sixteen enterprises with eleven attributes
are evaluated in this paper. The credit rating evaluating
criteria are grouped into the following three kinds: certainly,
could, uncertain belong to the set of “Good” corporate rating;
enterprises 2, 3 certainly belong to the set of “Good”
corporate rating. Results of this study show that the interest
expense ratio, debt ratio, receives months, sale months play
important roles in the overall assessment of enterprises.
These findings are invaluable for financial institutions for
their decision-making in the evaluation of corporate credit
rating. RST is a methodology which has demonstrated its
usefulness in the context of various cognitive science
processes.
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