Fuzzy Logic with Engineering Applications, 4th Edition

7Automated Methods for Fuzzy Systems

Measure what is measurable, and make measurable what is not so.

Galileo Galilei, circa 1630

For my part I know nothing with any certainty, but the sight of the stars makes me dream.

Vincent van Gogh, twentieth‐century painter

It is often difficult or impossible to accurately model complicated natural processes or engineered systems using a conventional nonlinear mathematical approach with limited prior knowledge. Ideally, the analyst uses the information and knowledge gained from prior experiments or trials with the system to develop a model and predict the outcome, but for new systems where little is known or where experimental analyses are too costly to perform (e.g., astronomy), prior knowledge and information is often unavailable. This lack of data on, or extensive knowledge of, the system makes developing a model using conventional methods extremely difficult and often impossible. Furthermore, forming a linguistic rule‐base of the system may be impractical without conducting additional observations. Fortunately, for situations such as these, fuzzy modeling is practical and can be used to develop a model for the system using the “limited” available information. Batch least squares (BLS), recursive least squares (RLS), gradient method (GM), learning from example (LFE), modified learning from example (MLFE), and clustering method (CM) are some of the algorithms available for developing a fuzzy model (Passino and Yurkovich, 1998). The ...