Most of us have had some contact with conventional logic at some point in our lives. In conventional logic, a statement is either true or false, with nothing in between. This principle of true or false was formulated by Aristotle some 2000 years ago as the Law of the Excluded Middle, and has dominated Western logic ever since. Of course, the idea that things must be either true or false is in many cases nonsense. The idea of gradations of truth is familiar to every one.
Fuzzy logic offers a better way of representing reality.
In fuzzy logic, a statement is true to various degrees, ranging from completely true through half-truth to completely false. The basic idea of multi-valued logic has been explored to some extent by a number of mathematicians in this century, but the real breakthrough was made by Prof. Lotfi Zadeh of the University of California in Berkeley. Most importantly, fuzzy theory was adopted wholeheartedly by the Japanese, and their advances in the field of fuzzy control have won the attention of engineers throughout the world. In this chapter we will consider fuzzy logic, with a continuous gradation of truth values ranging from false to true. We define the truth of a statement or value as being the confidence we have that the statement or value is correct.