Fuzzy Logic is a very powerful concept when applied to control systems. It allows control system designers to greatly reduce the number of rules necessary to deploy a desired control strategy. Additionally, it allows rules to be crafted in a very linguistic syntax. Finally, if properly designed, instabilities and hysteresis can be reduced or eliminated.

Classical Set Theory

Fuzzy Logic is a mathematical technique that greatly enhances the capability of the classical set theory. If you recall from simple set theory, problems were defined by grouping items into sets. For example, we may have six numerical members which can be categorized into two different sets for some reason. For the purpose of this example let’s assume the following arrangement:

Mathematically we write the fact that set A contains the numbers 3, 8 and 9 as { A: 3, 8, 9 }. Likewise, set B can be written { B: 3, 4, 7, 12 } since it contains the numbers 3, 4, 7, and 12.