Basic Fuzzy Set Theory
Fuzzy set theory and fuzzy logic provide a different way to view the problem of modeling uncertainty and offer a wide range of computational tools to aid decision making.
Abstract
Fuzzy set theory and fuzzy logic provide a different way to view the problem of modeling uncertainty and offer a wide range of computational tools to aid decision making. The mathematical basis for formal fuzzy logic can be found in infinite-valued logics, first studied by the Polish logician Jan Lukasiewicz in the 1920s. While the big economic impact of fuzzy set theory and fuzzy logic centers on control, particularly in consumer electronics, there has been, and continues to be, much research and application of these technologies in pattern recognition, information fusion, data mining, and automated decision making. All fuzzy set theory is based on the concept of a membership function. In many cases, the membership functions take on specific functional forms such as triangular, trapezoidal, S-functions, pi-functions, sigmoids, and even Gaussians for convenience in representation and computation. A neural network also acts as a membership function.