What is Fuzzy Logic?

Fuzzy logic is a type of mathematics and programming that more accurately represents how the human brain categorizes objects, evaluates conditions, and processes decisions. In the traditional logic system, an item that strictly does or does not belong to a group is called a set. For example, an animal either is or is not a dog. Fuzzy logic allows an object to belong to a set to a certain degree or with a certain confidence. Applications of fuzzy logic in contemporary computer systems are too numerous to cite, but they control things like heating mixtures and tooling parts.

The world is incredibly complex, both in breadth and depth. In some ways, it is difficult to adhere to the logical constraints of traditional set theory when describing how simple, daily decisions, such as cooking a roast or driving with traffic, are made. Yet computers are expected to make these decisions by simplifying or collapsing complexity and not taking into account uncertainty. Fuzzy logic was invented, and coined, by Dr. Lotfi Zadeh at UC Berkeley in 1965, when he was thinking about math, linguistics, and common sense.

To understand how fuzzy logic isn't a vague, tentative system, but can be used very practically to teach computers how to make decisions, an example may be useful. Starting with the rule, "No dogs in the house," logically this means that IF the object is a dog, THEN it is not to be in the house. Somehow, it can be deduced that a stuffed animal resembling a Dalmatian will be allowed in, but a real live Dalmatian won't. Some questions might remain, however, like whether seeing-eye dogs may be permitted, or whether animals that are half Husky and half wolf are permitted inside.

Fuzzy logic allows for these in-betweens when it comes to meeting requirements and initializing consequences. Instead of an animal absolutely belonging to the set of dogs, it can belong to a certain extent. A golden retriever might have an associated value of 1.0, as close to "completely" dog as possible, while a Chihuahua might have 0.8, due to its size. A seeing-eye dog might have a value of only 0.4, since it is often allowed where other dogs are not permitted.

This flexible system solves problems and controls machines that a simplistic logic system could not. The output, or the decision, is always clear and not fuzzy; in other words, the output is always "crisp." Eventually, the dog is either in the house or out on the porch — it's never halfway in. That is why "fuzzy" doesn't mean uncertain or unknown.