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About
Fuzzy Logic
The
Fuzzy Logic of A
Speeding Ticket
The
Fuzzy Logic of
Crossing The Street
THE MATHEMATICS OF APPROVING A LOAN APPLICATION
Approving a loan application, like issuing a speeding ticket, depends on a lot of factors, and every application has its own story.
This story begins with the applicant sitting across the desk from the loan officer. Will he get the loan? It depends.
SCORING THE APPLICATION
First the loan officer fills in the home improvement loan form. She collects information on a variety of factors - the amount required, and the address, phone number, assets, liabilities, income, years of employment and Beacon score of applicant. All the information is quantitative. Some entries are in the form of raw numbers. Others are Boolean checkboxes. The first spin is based on company policy.
The story according to company policy, like the story according to the letter of the law, is the simplest and easiest to spin. It is also the least reliable. Key qualitative information is missing.
The Mathematical Story According to Company Policy
Like the radar gun calculating the speed of the car, a software program behind the scenes uses the numerical values and Boolean numbers entered on the application to compute a raw risk score. According to company policy there is only one story. Like the speed of the car, the risk is either too high or it is not. The boundary is hard. In theory, the loan is approved unequivocally, or it is not.
In this story the raw score is 7. It would appear the applicant is eligible for the loan.
In practice, after the evidence has been collected and the raw score produced, the discretion of the loan manager kicks in, and a variety of stories become possible.
Qualitative factors enter into the equation - the history with the bank, credibility and demeanor of the applicant; the hunches, and impressions of the loan manager; the recommendation of employers and third parties.
Gray areas appear on the graph. They account for the qualitative measures
unaccounted for in the quantitative raw score. They are fuzzy numbers
that capture the qualitative information, as well as the nuances and subtleties
collected in enquiries - the conversations with the applicant, the phone
call to his employer, the opinion of branch manager, the experience of
loan manager.
On the graph of our story, the fuzzy number is the gray area "around
6" that contains the precise number 6 as well as the values close
to 6 that could be either "TOO HIGH" or "OK" to some
degree. This is where the judgement of the loan manager comes in.
The Mathematical Story in Practice
The "story according to company policy" indicates the risk is "OK", but certain qualitative factors lead the loan manager to believe the raw score is too high. There are inconsistencies in the stories the applicant told as he chatted as the form was filled in, and even though the numbers add up, there is something "fishy" about his demeanor.
The loan manager defers approval until due diligence can be exercised, and the bank is spared a bad loan.
Earlier in the day it was another story. A longstanding customer had came in before lunch to negotiate a loan. According to the information collected on the application form and company policy, the risk was "TOO HIGH". But the manager had dealt with this customer for years and knew him to be a good risk. The raw score seemed too low. The manager deferred stamping the application "Not Approved", and, in the long run, retained a valued customer.
If you were the driver, or the loan applicant, these stories would be about the judgement calls someone else made that affected you.
You also make judgement calls on your own behalf.
"Should I cross the street, or is the truck coming "too fast"?"
"Should I make this investment, or is it "too risky"?"
These stories can also be told mathematically.
decydeWARE™
Lorna Strobel Stewart Ph.D.
2/10/03
