Fuzzy Logic is a superset of Boolean, or classical, logic dealing with the concept of partial truth. While in Boolean logic everything can be expressed in binary terms (0 or 1, on or off, yes or no), fuzzy logic replaces classical truth values with degrees of truth that range between 0 and 1.
The subject was introduced by Lotfi Zadeh in the 1960s, and has been rather controversial since then. It is widely accepted within the engineering and computer science communities but generally rejected by mathematicians, a majority of which does not consider it a legitimate field of logic.