# Logic: Cold and Fuzzy

A recent post on the Good Math blog called “Fuzzy Logic vs Probability” reminded me of a coping skill that I take for granted, yet most people probably don’t know about. The post linked above is about the essential difference between probabilities and values in fuzzy logic.

Fuzzy logic is a sort of analog approach to Boolean logic. Boole constructed a rigid logical framework containing only two values: True and False. In Fuzzy logic, every statement has a rating of how true it is, from 0 to 100%. Decisions can therefore be made when there is not any binary certainty about the input parameters. The result is a degree (or percentage) of how true is the resulting compound statement.

But how can this be a coping skill?

Let’s say a spouse asks if you want to go out for dinner. If you absolutely refuse, or eagerly must, then the answer can be Boolean (Yes or No). But that No might just lead to an argument. A grudging Yes may breed resentment.

What if you are tired, but hungry, and not feeling sociable, nor like more driving, but also would like some entree that you are not likely to get at home, yet thinking about the money? You can go either way. One might call it 40% “want to go out”. By myself, under half is a “No”.

But here is the spouse, and the spouse has also had a hard day with different characteristics, and leans toward going out (as indicated by the issuing of the question). She might counter my 40% with a more urgent 80%. This 80% indicates a willingness to stay home, if I really want to. But the average (logical union) of our two values is 60%. So we go out, each understanding how strongly the other one feels about it.

If there is a near tie, we cast another ballot. As with a flipping coin in the air, one often has second thoughts about which way we want it to land. It does take a little practice to use percentages in gauging each others desires. But it really saves on arguments.

**Category**: Communication, Psychology Cognition, Whimsy

### About the Author (Author Profile)

A convoluted mind behind a curly face. A regular traveler, a science buff, and first generation American. Graying of hair, yet still verdant of mind. Lives in South St. Louis City. See his personal website for (too much) more.

Everything can be expressed in percentages. Well, 99 percent of things can be expressed in percentages.

Dan, you might like (or be good at) online texas hold 'em poker.

http://en.wikipedia.org/wiki/Poker_probability_%2…

Several years ago, I worked with a document processing system which employed fuzzy logic to read handwritten application forms.

The layman's description of how the system worked provides a straightforward insight into the operation of fuzzy logic systems.

In the system, monochrome scans of application forms were input into a program that identified individual character sub-images, then analyzed each sub-image 27 times. Each analysis (processed in parallel in special processes called operators) was biased to favor a certain subset of possible results. For example, operator 1 might be looking for the characters Q, W, E, R, T, 1, or 2 and operator 2 might be looking for O, W, F, B, I, Z, or 7. (Note that there is some overlap).

After all operators have reported the letters from their lists with the closest parameters, the results or tallied like votes to calculate a percentage score called the confidence level.

Say you have an applicant named Vadim Clio. The first pass yields results among the 27 operators like this

value-votes-confidence

"V"-8-29.6

"U"-8-29.6

"W"-6-22.2

"J"-2-7.4

"L"-1-3.7

"K"-1-3.7

"Z"-1-3.7

Next the parameters are tuned for the operators and the image is re-analyzed and the new results are:

"V"-10-37.0

"W"-8-29.6

"L"-5-18.5

"U"-4-14.8

The third pass results look something like :

"V"-18-66.6

"L"-9-33.3

The AI software used a "confidence threshold"

that would stop the output the first character with a confidence level above the threshold. our normal threshold level was 70, meaning that the output character would need at least 19 of the 27 votes.

In some cases, the AI couldn't resolve the character above the threshold, and after 9 passes, it would tag the character and its containing field for interactive editing.