Fuzzy Sets

Groups of Things That Match the Way We See and Think

In traditional logic, a set is used to describe a group of things, such as numbers greater than zero. The boundaries of these sets are precise. An item is either in a set or not in a set. Nothing can be partially in a set. Nothing can be in a set and also out of a set. This framework has worked well for logic and mathematics, but in everyday living, we are not usually so definitive in our use of sets.

Suppose you buy a new car. That night, is it still a new car? Yes, it is. A week later, is it a new car? Sure. How about 3 months later? Or 6 months? Somewhere along the way, you will feel that it's still a new car, but not as much a new car as the week you bought it. The boundary of "new car" is indistinct, or ..... fuzzy. Which is the word Lotfi Zadeh gave to the concept of partial membership in a set in 1965. To make the contrast clear, he gave the name "crisp" to the sets of classical logic. His ideas were heresy, and would never have been published if he hadn't been a highly respected engineering professor at Berkeley.

Let's continue talking about the real world. If you want to convey an idea, you often use fuzzy sets intuitively. If someone were to describe a man as small, you would probably picture someone well under six feet tall, and probably slim. However, if you were to hear someone refer to an NFL lineman as small, you would picture someone about six feet tall, around 200 pounds, and powerfully built. And you would, at the same time, think of him as a very large man. That football player would be in the set "small" and the set "large" at the same time, without causing confusion. Context would determine the boundaries of the sets.

People constantly use fuzzy sets and simple rules to make decisions in the real world. When you drive a car, you never know exactly how far you are from the left and right boundaries of your lane. In fact, you don't need to know and you don't want to know. It would be too much information. All you know is whether you are off centre a little bit .....or a lot. Then you move the steering wheel, a little bit ......or a lot. In the real world, fuzzy sets are not merely useful - they are essential. They prevent distractions and dithering caused by unnecessary precision. Business, industry and engineering have have benefited greatly from the use of fuzzy sets in decision-making.

Return To Fuzzy Expert Systems
Return To Home Page