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THE WIRED BANKER
Fuzzy Systems and Neuro-Computing in
Credit Approval
by Rashmi Malhotra and D.K. Malhotra
uzzy systems and neural networks are attracting growing interest
F
among both researchers and practitioners. These systems offer
advantages over traditional computational methods by offering
greater flexibility, greater tolerance of imprecise data, and an ability to
model nonlinear information of arbitrary complexity.
ary a lender would turn its
back on a system that could
learn to recognize patterns,
shave loan losses, improve consistency, and, at the same time, provide
greater flexibility. Today’s lender routinely blends statistical models and
other emerging techniques with rules
that have been developed through
experience. The choice of technique
depends on the complexity of the
institution as well as the size and the
type of loan.
Although analytical models are
useful, a consumer-loan officer often
uses rule-of-thumb to screen a loan
application. While such models as
empirically derived credit scoring
systems use the probability of default
to predict the relative creditworthiness of the applicant, they often cannot completely eliminate the human
element.
There remains some subjectivi-
N
ty regarding the selection of cutoff
scores and the evaluation of applicants that fall in the gray area
between accept and reject scores.
And while cutoff scores that are too
low may result in the acceptance of
too many applications that will ultimately turn into bad loans, scores
that are too high may drive away
business and shut the door on many
creditworthy customers.
To be more objective in evaluating loan applications, many institutions are now turning to artificial
intelligence (AI) techniques, such as
expert systems, artificial neural systems, and fuzzy logic.
Fuzzy logic consists of a variety of concepts and techniques for
representing and inferring knowledge that is imprecise, uncertain, or
unreliable. Fuzzy logic can create
rules that use approximate or subjective values and incomplete or
ambiguous data.
In addition, fuzzy logic may be
combined with other AI techniques,
such as neuro-computing and genetic algorithms. This concept is called
soft computing. Soft computing is
tolerant of imprecision, uncertainty,
and partial truth, thereby achieving
tractability, robustness, and low
solution cost.
Among the various combinations of methodologies in soft computing, the combination with the
highest visibility is that of fuzzy
logic and neuro-computing.
Neural networks, modeled after
the physical architecture of the
brain, are specialized hardware or
software that emulate the processing patterns of the biological brain.
Clearing Up Fuzzy Logic
As mentioned, fuzzy logic tolerates imprecise information and
© 1999 by RMA. Rashmi Malhotra is assistant professor of Management Information Systems at St. Joseph’s University in
Philadelphia, Pennsylvania. D.K. Malhotra is assistant professor of Finance at the School of Business Administration,
Philadelphia College of Textiles and Science, Philadelphia, Pennsylvania.
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The Journal of Lending & Credit Risk Management
July/August 1999
Fuzzy Systems and
Neuro-Computing
Figure 1
Fuzzy Logic Input/Output Map for Loan Evaluation
Loan
Application
Application
Status
Black
Box
Output Space:
Input Space:
• Accept the application.
• Reject the application.
• Possible acceptance after
further evaluation.
All the information provided
by the loan applicant.
uses the imprecision to solve problems that have not been solved
before. Fuzzy logic systems are
based on the way human beings
deal with inexact information.
Traditional computational techniques, such as statistical models
and neural networks, require precision—on/off, yes/no, right/wrong.
However, human beings do not
experience the world this way;
many of our activities and decisions
are inexact.
Fuzzy logic achieves a tradeoff
between significance and precision—
something that humans have been
managing for a very long time. This
technique deals with uncertainty,
using the mathematical theory of
fuzzy sets, and simulates the process
of normal human reasoning by allowing the computer to behave less precisely and logically than conventional computers do.
The rationale behind this
approach is that decision-making is
not always a matter of black and
white, true or false; it often involves
gray areas and “maybe.” Fuzzy logic
can create rules that use approximate
or subjective values and incomplete
or ambiguous data. By expressing
logic with some carefully defined
imprecision, fuzzy logic is closer to
the way people actually think than
traditional if/then rule-based expert
systems and neural networks, which
are modeled after the physical architecture of the brain.
As illustrated in Figure 1, fuzzy
logic can be considered the black
box that maps the decision to
accept, reject, or further evaluate a
loan application.
The input variables are the
information provided by the loan
applicant, and the output space is
the status of the application. The
loan officer is advised to accept the
application, reject the application,
or gather more information for further evaluation.
Figure 2 illustrates the architecture of a fuzzy inference system for
credit evaluation. This architecture
corresponds to the black box of
Figure 2
Figure 1. The system processes a
loan application using if/then rules,
and the output of the system is a
recommendation to the loan officer.
Figure 2 displays sample rules
that can be used by a loan evaluation system. Suppose a bank
receives an application for a mortgage loan. A loan application
includes such information as the
applicant’s age, housing, length of
time at address, total income, number of credit cards, number of
dependents, job time, co-maker on
other loans, total debt, and monthly
rent/mortgage payments. The loan
officer further collects information
on the number of inquiries for an
applicant and a credit rating for the
applicant. On the basis of this information, the loan officer calculates
an applicant’s total-payments-tototal-income and total-debt-to-totalincome ratios.
According to economic rationality, the loan officer should consider
three factors—the ratio of totalpayment-to-total-income, the ratio of
total-debt-to-total-income, and the
credit rating. The output of the system
Fuzzy Inference System for Credit Evaluation
Ratio 1
Ratio 2
Credit Rating
Application
Status
If ratio 1 is high or very high, then reject the applicant.
If ratio 1 is medium or high and ratio 2 is not very high and credit rating is medium,
then accept the applicant.
If ratio 1 is low and ratio 2 is low and credit rating is good, then accept the applicant.
Ratio 1
very low,
low,
medium,
high, and
very high
Ratio 2
very low,
low,
medium,
high, and
very high
Credit Rating
very poor, poor,
good, very
good, and
excellent
Application Status
accept, reject,
and conditional
acceptance
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Fuzzy Systems and
Neuro-Computing
can be to accept the application, reject
the application, or recommend further
evaluation of the application for possible acceptance.
The neuro-fuzzy system uses a
membership function that defines
how each of three input variables
(ratio 1, ratio 2, and credit rating) is
mapped to a membership value
between 0 and 1. For the mortgage
loan example, Table 1 displays the
class intervals of the input variables. As illustrated, ratio 1 can be
described as very low, low, medium, high, or very high. Similarly, as
shown in part B of Table 1, ratio 2
also varies between 0 and 1. Unlike
ratio 1 and ratio 2 that lie between 0
and 1, credit rating varies between 1
and 4, and can be described as very
poor, poor, good, very good, and
excellent. Therefore, we can use a
mathematical/statistical distribution
system to map the credit rating
between 0 and 1. The fuzzy system
uses these input variables and a set
of rules to process a loan application. Table 2 illustrates the class
intervals of output.
A fuzzy system works in five
steps. The system processes imprecise information; therefore, for a
given set of input variables it works
through all the rules.
So Happy Together
Fuzzy logic and neural networks are complementary technologies in the design of intelligent systems. Each method has its pros and
cons. For example:
• Artificial neural systems suffer
from their inability to explain
the steps by which they reach
decisions and their inability to
incorporate rules into their
structure. Neural fuzzy systems
address some of the shortcom26
ings of artificial neural intelligence tools.
• Fuzzy logic techniques often
deal with issues such as reasoning on a higher level than neural networks. However, since
fuzzy systems do not have
much learning capability, it is
difficult for a human operator
to tune the fuzzy rules and
terms.
A promising approach that
reaps the benefits of both fuzzy systems and neural networks is to
merge fuzzy logic and neural networks into an integrating system.
mate cardholders who had slightly
altered their spending, angering the
bank’s customers and wasting the
bank’s resources. The bank then
turned to a neural network fraud
detection system application devel-
Current Applications for the
Financial Services Industry
Neural network technology is
currently being used in mortgage
lending to underwrite both loans and
mortgage insurance. Foster Quality
Conley developed AQUARIUS
(Automated Quality Control Artificial
Intelligence Underwriting System) to
meet lenders’ demands for automated
underwriting systems that qualify
mortgages for sale in the secondary
market.
California-based Sears Savings
Bank is experimenting with a neural
net application to help its mortgage
underwriters evaluate loan applications. After being fed extensive historical data on mortgages, the neural net was trained to recognize patterns for successful and unsuccessful loans.
Fraud-detecting neural networks
have been used successfully in limiting losses to issuers of credit cards.
Mellon Bank in Pittsburgh,
Pennsylvania, uses a neural network
system to detect credit card fraud.
The bank used to employ an expert
system for this purpose; however,
that system flagged too many legiti-
The Journal of Lending & Credit Risk Management July/August 1999
Table 1
Class Intervals of the
Input Variables
Part A: Ratio of Total Payment to
Total Income (Ratio 1)
Ratio 1
Value
Very low
<=0.30
Low
Medium
>=0.30 and <=0.50
>=0.50 and <=0.60
High
>=0.60 and <=0.75
Very high
>=0.75
Part B: Ratio of Total Debt to Total
Income (Ratio 2)
Ratio 2
Value
Very low
Low
<=0.25
>=0.25 and <=0.50
Medium
>=0.50 and <0.65
High
Very high
>=0.65 and <=0.80
>=0.80
Part C: Credit Rating
Credit Rating
Value
Very poor
Poor
<=0.60
>=0.60 and <=1.00
Good
>=1.00 and <=2.25
Very good
Excellent
>=2.25 and <=3.00
>=3.00 and <=4.00
Table 2
Class Interval of
Application Status
Application
Status
Value
Accept
<=0.40
Possible accept
>=0.40 and >=0.60
Reject
>=0.60 and <=1.00
Fuzzy Systems and
Neuro-Computing
oped by Nestor Corporation of
Providence, Rhode Island. The network is taught to recognize irregular
patterns in charge card purchases and
to evaluate fraudulent transactions.
GE Capital and Colonial Bank,
among others, also have installed
neural networks to reduce credit
card fraud. And Fidelity
Investments, which has used a neural network to help pick stocks for
its Stock Selector fund since 1989,
has outperformed the S&P 500
Index by 2-7% each quarter for
three years.
In the past few years, the number and variety of applications of
fuzzy logic in the financial services
industry have grown rapidly. For
example, a Wall Street firm developed a system that selects companies
for potential acquisitions, using language stock traders understand. An
international investment company is
using a combined fuzzy logic and artificial neural network system
(FuzzyNet) to forecast the expected
returns from stocks, cash, bonds, and
so forth, to determine the creditworthiness of various countries and estimated performances of key socioeconomic ratios. Then, it selects specific
stocks based on company, industry,
and economic data. The final stock
portfolio must be adjusted according
to the forecast foreign exchange rates,
interest rates, and so on. The firm
found that predicted and actual returns
are statistically comparable.
Some academic studies illustrate the use of fuzzy logic for individual asset allocation and to make
insurance pricing decisions that
consistently consider supplementary
data, including vague or linguistic
objectives of the insurer. Stock
Smart uses a fuzzy logic system to
help select mutual funds that come
closest to meeting an investor’s
standards. The U.K. stock exchange
uses Intelligent Alerting System,
which uses genetic algorithms, and
fuzzy logic to spot fraudulent trading activities among the 60,000
transactions made each day.
Barclays Bank has invested three
million pounds sterling in a neural
network system aimed at combating
fraud from retailers.
Conclusion
Although traditional artificial
intelligence methods, such as expert
systems, have been used extensively
by many organizations, artificial
neural systems and fuzzy logic are
relatively new techniques to capture
the attention of the finance community.
Fuzzy logic offers a natural and
logical approach that does not
reflect its far-reaching complexity.
Further, fuzzy logic is flexible. It
allows the decision-maker to make
an allowance for the unexpected,
depending on the functionality
required by a loan application.
Besides, fuzzy logic is tolerant of
imprecise data, and fuzzy reasoning
builds the imprecise understanding
into its basic processes.
Fuzzy logic can model nonlinear functions of arbitrary complexity. The decision-maker can create a
fuzzy system to match any set of
input-output data. In addition, fuzzy
logic can be built on top of the
experience of experts.
In direct contrast to neural networks, which take training data and
generate opaque, impenetrable models, fuzzy logic develops models that
represent the common sense reasoning of the loan officers, in the form
of if/then rules.
Finally, fuzzy logic can be
blended with conventional loan
evaluation techniques. A fuzzy system can be developed that uses statistical and neural network models
in addition to the intuitive knowledge of the loan officer represented
as rules.
Therefore, fuzzy systems do
not necessarily replace conventional
loan evaluation methods. In many
cases fuzzy systems augment them
and simplify their implementation.
These systems offer a promising
solution to the loan officers who
require a system that can use mathematical models as well as humanbased reasoning. Further, neurocomputing—a combination of neural networks and fuzzy systems—
offer even more flexible decisionmaking tools. Neural networks have
the capability to learn by experience
that is augmented by the human reasoning of the fuzzy systems.
Finally, practitioners, using an
off-the-shelf fuzzy toolbox offered
by software vendors, such as MATLAB and Brainmaker, can develop
fuzzy inference systems. The software is user-driven and offers an
interactive interface that does not
require any programming. The user
can fill in the mathematical functions and their parameters, and
write the rules in English. The software develops the fuzzy inference
system.
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Interview: Ann Goodbody
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The Journal of Lending & Credit Risk Management January 1999