Intro Binary Logic Fuzzy Logic Fuzzy Set Chicalm Washing Machine History Books

Playground

Rapunzel

Dido's Problem

Pythagoras

Trigonometry

Smart Joe

Fuzzy Logic

Cryptography

Mathematicians

Today many houshold appliances have fuzzy logic built into them to make their use easier. You can find fuzzy logic in shower heads, rice cookers, vacuum cleaners, and just about everywhere. So you can get an idea how these machines work, we'll look at this simplified model of a fuzzy washing machine.

Like a real fuzzy washing machine would, our model first tests how dirty the laundry is. Once it knows how dirty the laundry is, it can easily calculate how long it should wash it. To calculate this it uses the graph below:

First it always takes a base of 10 minutes. It does this so that people are happy with its work even if they put completly clean laundry in to wash. It then calculates to what degree it is dirty. If it is 100% dirty it adds two minutes per piece of laundry. Of course a real washing machine would just do these calculations in the end, but our model does it for each individual piece so you can keep track of what is going on easier.

So if you now add a piece which is only 50% dirty, it will add 50% of 2 minutes; it adds 1 minute instead of 2 minutes to the base of 10 minutes.

Our washer, however, doesn't only check for dirt but also for grease. Laundry which is greasy has to be washed longer too. Since the laundry can be greasy and dirty at the same time, we have to put them on the same graph. When we do this, we get a graph like the one below:

On the graph to the right, you can see once more the base of ten minutes. The point 0,0 is where the laundry is completely clean; non-dirty and non-greasy. The point 0,1 is where the laundry is non-greasy, but dirty. The point 1,0 is where it is greasy but not dirty and 1,1 is greasy and dirty. The washing machine adds 2 minutes per piece for 100% dirty or 100% greasy and 4 minutes for 100% dirty and greasy.

So now if you have a piece of laundry which is 100% dirty and 50% greasy, you first go to the point 0,1 (100% dirty) and then go halfway towards point 1,1. If the cube would contain more information, you could now see that the washer has to wash it for 3 minutes more than the base of 10 minutes.

Add a piece of laundry to the washer!

The washing machine would take minutes to wash

These are only two aspects a fuzzy washing machine might take into account when washing. A real one would also check to see how much soap it needs, how much water to add, how fast and which direction it should spin, etc. If we wanted to graph every calculation a fuzzy machine makes, we would need a pretty complex hypercube. So we'll just limit ourselves to grease and dirt.

There has been a boom for fuzzy machines in the last two decades. This is not only because they can do things which we humans had to do ourselves until now, but also because they're much cheaper to build than normal binary machines. But the idea on which fuzzy logic is based, A can equal not-A, isn't as modern as the fuzzy machines we use today.