Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. By contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1. Furthermore, when linguistic variables are used, these degrees may be managed by specific (membership) functions. Fuzzy logic has been applied to many fields, from control theory to artificial intelligence.

Fuzzy logic has two different meanings. In a narrow sense, fuzzy logic is a logical system, which is an extension of multi-valued logic. However, in a wider sense fuzzy logic is almost synonymous with the theory of fuzzy sets, a theory which relates to classes of objects with unsharp boundaries in which membership is a matter of degree. Some general observations about fuzzy logic are:

• Fuzzy logic is conceptually easy to understand – The mathematical concepts behind fuzzy reasoning are very simple. Fuzzy logic is a more intuitive approach without the far-reaching complexity.

• Fuzzy logic is flexible – With any given system, it is easy to layer on more functionality without starting again from scratch.

• Fuzzy logic is tolerant of imprecise data – Everything is imprecise if you look closely enough, but more than that, most things are imprecise even on careful inspection. Fuzzy reasoning builds this understanding into the process rather than tacking it onto the end.

• Fuzzy logic can model nonlinear functions of arbitrary complexity – a Fuzzy system can be created to match any set of input-output data. This process is made particularly easy by adaptive techniques like Adaptive Neuro-Fuzzy Inference Systems (ANFIS), which are available in Fuzzy Logic Toolbox software.

• Fuzzy logic can be built on top of the experience of experts – In direct contrast to neural networks, which take training data and generate opaque, impenetrable models, fuzzy logic lets user rely on the experience of people who already understand the system.

• Fuzzy logic can be blended with conventional control techniques – Fuzzy systems don’t necessarily replace conventional control methods. In many cases fuzzy systems augment them and simplify their implementation.

• Fuzzy logic is based on natural language – The basis for fuzzy logic is the basis for human communication. This observation underpins many of the other statements about fuzzy logic. Because fuzzy logic is built on the structures of qualitative description used in everyday language, fuzzy logic is easy to use.