Our scientific world prefers to have clearly measurable edges, but the reality is that in life, fuzziness is more prevalent than definiteness. Aristotle formed the law of the excluded middle that has been a very important help to us understanding our world. His law states that everything is A or not A. So, if A is North America, then everything is either in North America (A) or is outside North America (Not A). There are only the two options, there is no middle ground because it has been excluded. There is nothing that can be beyond A and not A.  But, is it really so clear?

If there is enough snow, we can build a snowman. The snowman can be built with many details on the face and clothing. After it has been built, the weather slowly wears away at the snowman, so its shape becomes less and less definite; less and less like a snowman and more like a mere blob of snow. There is no point at which we can all a sudden say there is now no longer a snowman. The movement from snowman to blob has no clear edges, it is fuzzy.

Furthermore, we can rate the degree of fuzziness. If something is a definite fact, it is given a value of 1. If it is definitively untrue, it is given the value of 0. For our snowman, if it is a perfect snowman it has the value of 1 and if it is a blob it has a value of 0. As the weather gradually wears away its snowmanness, its fuzzy value slowly moves from 1 down to 0.

Our language is full of fuzziness so that we can describe the fuzziness of the world in which we live. All words such as “probably, almost, quite, fairly, and round about”. Even words we would think are straight forward and precise are not so. The simple word car is actually a fuzzy term. There are so many different types of car. Some types of car are more typical of what comes to mind when we think of car. Others such as three wheeled cars, three wheeled motorcycles, campervans, and right through to skateboards and unicycles have a degree of ‘carness’. The degree of ‘carness’ can be measured on a scale of 0 to 1 as with our snowman.

The speed limit set on our roads are precise and discrete. If a limit on a stretch of highway is 100 km/hr, it does not mean that 99 km/hr is a safe speed at which to travel and 101 km/hr is a dangerous speed.

The reality is that there is even a risk of an accident at 5km/hr even though the level of risk is low. As we increase the velocity towards 100km/hr the risk increases more and more. As the velocity increases beyond 110 km/hr the level of risk increases even more until at very high speed the risk becomes very high.

As in so many aspects of life, the reality is fuzzy, but we try and control the situation by discrete rules. The risk of accident varies, but the rule is that a somewhat arbitrary 100km/hr is chosen as the limit.

Many of the machines we use on our daily life also operate on fixed rules to try and cope with a fuzzy environment. A thermometer on a heater turns off when the temperature reaches a certain point and turns on again when the temperature falls below another predetermined level. Imagine how much more effective the machine would be if we could use fuzzy rules to match a fuzzy environment. In fact such machines do exist.

We can notice similarities between fuzzy logic and Quantum Mechanics and the Heisenberg principle of uncertainty. Heisenberg found that at very small sub-atomic levels we are not able to measure what we see with the same level of certainty that we can measure things we see at our everyday mesoscopic level. He found that if we measure the position of a sub atomic particle, we can no longer measure its momentum and if we measure the particle's momentum, we can no longer measure its position. The very act of measuring the particle changes it and makes the complete measurement impossible. Fuzzy logic also shows that the world is not as measurable as we had thought, but it demonstrates it directly in the mesoscopic world rather than only at sub atomic levels.

In the 1960’s Lotfi Zadeh formulated the idea of Fuzzy Sets. He proposed that we could form a membership curve for the set of tall men. Men who were indeed very tall would have a high level of membership of the group, while a short man would still be on the membership curve, but have a low level of membership. The membership curve for short men would be a mirror reflection of the curve for tall men. Where tall men have a low level of membership of the short men curve, short men have a high level of membership.

Fuzzy logic also uses the ideas of patches. While it is often very difficult to predict the operation of a particular system over the whole range of its operation, we can put a patch over a part of the system’s operation. If the patch describes the operation very accurately, then the patch is very thinly wrapped around that part of the graph of the system’s operation. If the patch is not as accurate then the patch is wider.  The more patches you have the more accurate it is. With the patches there is no need to know what is actually causing the behaviour of the system as long as they can give enough information about how the system operates in the range of the patch.

With a thermostat the heat either turns off or turns on depending on whether the ambient temperature is in the range set by the thermostat. Using fuzzy sets each patch can be set with its own rules. If the temperature is only just above the ideal, the heater can be set to turn on a low level of heat, but the further the temperature drops, the higher the heating unit is set. Different levels of heat can be set depending on which patch is activated. A fuzzy system will return to the desired temperature quicker and will respond more efficiently than a conventional system. You can see how the same fuzzy principle of patches can be applied to other systems such as getting a train to stop at the right place on a platform, toasting bread to just the right amount, washing clothes or vacuuming the floor more efficiently.

Other applications include air conditioner units, car brakes, concrete mixers, photocopiers, microwave ovens, refrigerators, stock trading, and character recognition on computers where a scanned, or handwritten, letter or number can be decoded and understood by the computer.

Human decision making may well operate on a fuzzy system. Do we in fact intuitively look for a fuzzy weighted average of the various factors to be taken into account in each possible choice of action? And does our justice system actually work on a fuzzy basis. We have a set of rules called laws just as fuzzy systems have rules, but the interpretation of those rules appears to be decided on through fuzzy weighted averages. A judge will look at the rule of law and then consider mitigating factors that would lead to a lighter punishment and aggravating factors that would lead to a more severe punishment. All these factors are weighted and balanced out in the final decision.

Just as complex system can become adaptive and find ways to enhance their effectiveness without intervention from outside, there are fuzzy adaptive systems which can adapt their own rules to make the system more efficient. It checks the effectiveness of its rules and interpretation and weighting of the rules to find more effective combinations. The longer the systems operates and the more data it processes, the more accurate its ability to judge the most efficient way for the system to operate.

Human learning could well be fuzzy, We certainly notice that the more we do a particular activity or practice and activity, we become more effective at it. Could we be adapting the rules and weightings we have in our mind intuitively, so they become more accurate and effective. This could even be reflected in the physiology of the brain. Perhaps the changes of fuzzy rules are reflected in the changes in the connections between the neurons in the brain.