Fuzzy logic allows us a gradual and continuous transition from 0 to 1, rather than an abrupt and crisp change between binary values of 0 to 1. The traditional logic and set theory deal with only discrete values. For example, an element in an ordinary(crisp) set either belongs to the set or does not belong to the set. Simply in this example, an element belongs to the set is represented by a 1 and an element does not belong to the set is represented by a 0. In ordinary logic a situation is either true or false. But in fuzzy logic, an element can partially belong to a set, for example with a degree of 65%.
If you are interested in fuzzy logic, I suggest you to study the chapter about fuzzy logic in the book Fundamentals of the New Artificial Intelligence by Toshinori Munakata. It is a complete and adequate source. The book also includes other systems about artificial intelligence.
In the next post, I will develop a simple application which examines the basics of fuzzy logic.