Fuzzy Logic

Is something completely true or completely false? Is it a lie or is it the truth? Am I rich or am I poor? Aristotle's Law of the Excluded Middle, otherwise known as Boolean, dominates western logic. A Boolean value is either true or false, yes or no, and 0 or 1. Most of us are familiar with the different gradations of truth. Fuzzy logic offers an "in between" value. It is a statement true to different gradations, or degrees.

As in Aristotle's way of thinking, there is either fast or slow. But with fuzzy logic, there can be slow, medium, fast, etc. This new kind of logic has a large impact on patterns of reasoning. Fuzzy logic is helpful in constructing expert systems, which are real world human reasoning.

Professor Lotfi Zadeh of the University of California in Berkeley made a major breakthrough in 1965 on the theory of fuzzy sets. He proposed that a fuzzy set is one where its objects can belong to different degrees, or grades of membership. Another term for grades of membership is our level of "confidence". An ordinary set would be called "crisp", which means that any object either belongs or not belongs, or is true or false, etc. There are no gradations of truth in an ordinary set. However, in a fuzzy set, it is a different kind of truth. It is one where an object can belong into one group not entirely, but to a certain degree.

A major aspect of fuzzy logic is fuzzy number. It is an ordinary number whose exact value is uncertain.
This is a fuzzy two:

We can say that our confidence that numbers 1.5 or less belong to the fuzzy 2 is zero as is that for numbers greater than 2.5. Our confidence for numbers 2 is 1000. Hedges in math circles are descriptive terms such as "roughly", or "close", or "nearly", etc. The graph above is "roughly 2". Fuzzy numbers enable us to make approximate comparisons and approximations.

Fuzzy logic is useful in the development of techniques for autonomous navigation in real world environments. It enables one to cope with the uncertainty in a natural environment. Fuzzy logic has features that make it an adequate tool to address the problem in autonomous navigation for the real world.

Fuzzy logic is used to control many systems. They range from elevators to braking systems, to your air-conditioning system, and to weaponry.

Fuzzy logic has a few restrictions and limitations. For one, it needs a large amount of data to start with. Second, it does not provide accurate nor precise sizing-only crude estimates.