Although alternative approaches such as genetic algorithms and neural networks can perform just as well as fuzzy logic in many cases, fuzzy logic has the advantage that the solution to the problem can be cast in terms that human operators can understand, such that that their experience can be used in the design of the controller.
[1] Fuzzy logic was proposed by Lotfi A. Zadeh of the University of California at Berkeley in a 1965 paper.
Other research followed, with the first industrial application, a cement kiln built in Denmark, coming on line in 1976.
Work on fuzzy systems is also proceeding in North America and Europe, although on a less extensive scale than in Japan.
[7] These systems can be employed to control complex, nonlinear dynamic plants, for example, human body.
Given "mappings" of input variables into membership functions and truth values, the microcontroller then makes decisions for what action to take, based on a set of "rules", each of the form: In this example, the two input variables are "brake temperature" and "speed" that have values defined as fuzzy sets.
From three to seven curves are generally appropriate to cover the required range of an input value, or the "universe of discourse" in fuzzy jargon.
"Extremely" cubes the values to give greater narrowing, while "somewhat" broadens the function by taking the square root.
There are several ways to define the result of a rule, but one of the most common and simplest is the "max-min" inference method, in which the output membership function is given the truth value generated by the premise.
The "centroid" method is very popular, in which the "center of mass" of the result provides the crisp value.
Notice how each rule provides a result as a truth value of a particular membership function for the output variable.
The input and output variables map into the following fuzzy set: —where: The rule set includes such rules as: In practice, the controller accepts the inputs and maps them into their membership functions and truth values.
The appropriate output state is selected and assigned a membership value at the truth level of the premise.
A fuzzy set is defined for the input error variable "e", and the derived change in error, "delta", as well as the "output", as follows: If the error ranges from -1 to +1, with the analog-to-digital converter used having a resolution of 0.25, then the input variable's fuzzy set (which, in this case, also applies to the output variable) can be described very simply as a table, with the error / delta / output values in the top row and the truth values for each membership function arranged in rows beneath: Suppose this fuzzy system has the following rule base: These rules are typical for control applications in that the antecedents consist of the logical combination of the error and error-delta signals, while the consequent is a control command output.
The microcontroller has to make decisions based on brake temperature, speed, and other variables in the system.
[10] In spite of the appearance there are several difficulties to give a rigorous logical interpretation of the IF-THEN rules.
Before an Artificial Intelligence system is able to plan the action sequence, some kind of model is needed.
[13] A qualitative simulation isn't able to determine the correct follow up state, but the system will only guess what will happen if the action was taken.
The Fuzzy qualitative simulation can't predict the exact numerical values, but it's using imprecise natural language to speculate about the future.
It takes the current situation plus the actions from the past and generates the expected follow up state of the game.
The output of the ANFIS system isn't providing correct information, but only a Fuzzy set notation, for example [0,0.2,0.4,0].
[14] Fuzzy control systems are suitable when the process complexity is high including uncertainty and nonlinear behavior, and there are no precise mathematical models available.
Successful applications of fuzzy control systems have been reported worldwide mainly in Japan with pioneering solutions since 80s.