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About
Fuzzy Logic
The
Fuzzy Logic of A
Speeding Ticket
The Fuzzy
Logic of A
Loan Application
THE MATHEMATICS OF CROSSING THE STREET
You are at the curb deciding, "Should I cross the street?" Well, it depends.
AT THE CURB
The walk light is on, but you see a truck approaching fast. "How fast?"
There is no exact number. Instead, there are an infinite number of possibilities - from 1kph to over 100kph and everything in between. You don't have a radar gun, so instead you watch the truck for a second or two, and sum its speed up in two words "very fast". That is good enough.
Your senses have told you the truck is coming very fast, but you need more information before you can decide whether or not to risk crossing. "How far down the street is the truck?" "Is it slowing down?" Again, there are no exact numbers, so you sum up the situation - "close", "not slowing quickly enough".
Somehow your brain adds "fast" + "close" + "not slowing quickly enough", and warns you instantly that the risk is "high". It is purely cognitive process. It involves a complex combination of sensory information and experience.
The Mathematical Story
Since there are no exact numbers in this story, the mathematical version must be told with fuzzy numbers. The four fuzzy graphs are the story line.
In the first graph, the third triangle is the fuzzy number "fast", and means all the possible speeds between 50 to 100kph that are fast to some degree. In the second graph the first region is the fuzzy number "close". This covers all the possible distances between 100 to 500 meters that are close to some degree. In the third graph the first region is the fuzzy number "slowly", or conversely, "not quickly". This covers all the possible rates of deceleration that are slow to some degree.
Add them up and use common sense, or fuzzy logic, and the risk is "too high". The fourth graph shows this conclusion.
But, the process is still not quite over. "Should I wait or cross?"
You have to make the decision.
Risk tolerance leads to different spins and endings.
If you walk with a cane, you reason, "The risk is high, so I'll wait." You watch as the truck runs the red light.
If you are a jogger, impatient to cross, you disregard the evidence, step into the intersection, and jump back just in time to save your life.
decydeWARE™
Lorna Strobel Stewart Ph.D.
2/10/03
