Fuzzy Systems
Fuzzy systems are fundamental methodologies to represent and process linguistic information, with mechanisms to deal with uncertainty and imprecision. Take for instance the task of modeling a driver parking a car. The closer we look at this problem, the more we realize the difficulty of writing down a rather concise mathematical model to describe this action. Yet, we actually can describe the action of this driver in terms of simple linguistic rules. With such remarkable attributes, fuzzy systems have been widely and successfully applied to control, classification and modeling problems (Mamdani, 1974) (Klir and Yuan, 1995) (Pedrycz and Gomide, 1998).
Although simplistic in its design, the identication of a fuzzy system is a rather complex task that comprises the identication of (a) the input and output variables, (b) the rule base (knowledge base), (c) the membership functions and (d) the mapping parameters.
Usually the rule base rule base consists of several IF-THEN rules, linking input(s) and output(s). A simple rule of a fuzzy controller could be:
IF (TEMPERATURE = HOT) THEN (COOLING = HIGH)
The numerical impact/meaning of this rule depends on how the membership functions of HOT and HIGH are shaped and defined.
The construction and identification of a fuzzy system can be divided into (a) the structure and (b) the parameter identification of a fuzzy system.
The structure of a fuzzy system is expressed by the input and output variables and the rule base, while the parameters of a fuzzy system are the rule parameters (defining the membership functions, the aggregation operator and the implication function) and the mapping parameters related to the mapping of a crisp set to a fuzzy set, and vice versa. (Bastian, 2000).
Much work has been done to develop or adapt methodologies that are capable of automatically identifying a fuzzy system from numerical data. Particularly in the framework of soft computing, significant methodologies have been proposed with the objective of building fuzzy systems by means of genetic algorithms (GAs) or genetic programming (GP).
Read more about this topic: Genetic Fuzzy Systems
Famous quotes containing the words fuzzy and/or systems:
“What do you think of us in fuzzy endeavor, you whose directions are sterling, whose lunge is straight?
Can you make a reason, how can you pardon us who memorize the rules and never score?”
—Gwendolyn Brooks (b. 1917)
“The skylines lit up at dead of night, the air- conditioning systems cooling empty hotels in the desert and artificial light in the middle of the day all have something both demented and admirable about them. The mindless luxury of a rich civilization, and yet of a civilization perhaps as scared to see the lights go out as was the hunter in his primitive night.”
—Jean Baudrillard (b. 1929)