Teaching Fuzzy Logic

Problem: In life, we commonly find that a little bit of bad information can be far worse than no information at all. Here are some examples of what I mean:

1. One time we were Geocaching, which means we were looking for a small "treasure" that was hidden in about a 20 foot radius. A friendly jogger came by and told us that she had seen people looking for this cache before, and we needed to be looking much deeper into the woods. This turned out to be incorrect, which led to our spending about an hour unsuccessfully searching for the hidden container. (We found it on a subsequent trip, after getting more reliable information).

2. A few years ago, there was a sniper loose in our metropolitan area. Ten people were killed, and three others critically injured, including one man who was filling his gas task a few miles from our home. The police identified a white box truck as the likely vehicle, and weeks went by with massive searches of white box trucks. Traffic was tied up for miles, etc. The suspects were ultimately apprehended in a dark blue Chevrolet Caprice sedan.

3. How often do you hear a company say that you can find more information regarding a certain topic on their website? Then you go to the site, and search hopelessly throughout the site with nothing to be found on the topic - certainly nothing plainly visible on the front page. You would have been better off searching quickly on the site, then just going somewhere else for the information.

Solution: Computers fare much better than people when they are given small amounts of incorrect information. This is because they can implement algorithms based on "Fuzzy Logic", which essentially allows certain facts to be temporarily overlooked or reduced in value when other facts seem to give a more compelling solution. A classic example is those 20 Questions games. Surely you have been amazed that the computer often can ultimately identify your item, even in some cases where you tell it an outright lie for 1 or 2 questions.

Children are not taught fuzzy logic in school. Wouldn't it be interesting to have some logic questions for students to answer where they are presented with some facts, and told that 1 of the facts is wrong? It seems to me that this would be a great skill to develop, given the reality of the world. With so many of the issues you hear discussed today, you need to be able to develop sound conclusions when there are red herring facts vying for your attention. Global warming and evolution are two examples that jump to mind.

So let's get this new brand of teaching started. See if you can solve the example below for x and y! (Exactly one of the statements is wrong)

2x + 3y = 27
4x + 4y = 40
x + y = 9
2y - 2x = 8
5x + y = 22