Just what is Fuzzy Logic? Fuzzy Logic was actually invented by Lofti Zadeh way back in 1965. Despite its name, Fuzzy Logic is not the science of fuzzy thinking combined with fuzzy conclusions :-). Fuzzy Logic is a method for modeling and reasoning about imprecise or approximate concepts. Traditional logic, where concepts must be true or false, zero or one, has trouble at the boundaries of a problem: Is the water hot or cold? It's neither and both, it is somewhat hot. Fuzzy logic concerns itself with the boundaries of a concept, things can be "somewhat true" and "sorta false". Fuzzy Logic reduces system complexity by avoiding the complex mathematics and logic necessary to solve problems at these boundary conditions using traditional, exists/not exists, logic. It is able to approximate the behavior of problems that are poorly understood or non-linear.
Fuzzy Logic also exhibits another desirable characteristic, it allows the user to represent or model the problem linguistically. Fuzzy Logic allows reasoning about the problem in ways natural to the user: Is the temperature hot? How long is the project duration? Using linguistic variables (similar to regular variables like X and Y except they take values like "cold" or "not very long"), Fuzzy Logic provides a closer mapping between the actual, real world, problem and the computer representation of the problem.
Altogether, Fuzzy Logic provides a mechanism for reducing development time, modelling complex non-linear systems, and increasing comprehension and understanding of the solutions made.