Computational Intelligence, Theory and Applications - International Conference 9th Fuzzy Days in Dortmund, Germany, Sept. 18-20, 2006 Proceedings

Fuzzy Control – Expectations, Current State, and Perspectives (p. 667)

Mirko Navara and Milan Petr´ýk

Summary.

We summarize the history of fuzzy sets. We try to find the reasons why fuzzy control has been so successful in applications. This is mainly explained by the fact that fuzzy logic created an alternative to exact computation and it better fits to the human way of reasoning.

We point out some aspects in which current fuzzy systems are not completely satisfactory and directions in which they should develop in the future.

Key words:

Fuzzy set, Fuzzy control, Computational complexity, Fuzzy arithmetic, Stability.

The idea of partial truth and partial membership is old and it has been rediscovered many times (e.g., (4, 7, 13)). However, the seminal paper (28) has opened a new epoch of its rapid development. Our first question is why exactly this work initiated a revolution if many theoretical results (see (4, 24)) have been derived before and remained almost unnoticed.

One reason is that Zadeh expressed this idea in a way accepted by experts in many fields, not only theoretical, but also applied, even by engineers. The preceding papers were recognized only by a limited community of mathematicians. Now the principle was expressed in a way understandable to everybody and in a context drawing new horizons and capabilities of the new technology based on it. It might have been crucial that the applications in control theory followed very soon (14, 26, 29).

Their success ensures permanent interest of industrial partners and financial support of this field. The second reason of success of fuzzy logic in Zadeh’s approach is the state of control theory in the sixties. Preceding development of computers and cybernetics has brought ambitious expectations which have been satisfied only partially. The rapid development of control theory, as initiated by Wiener, has slowed down.

It solved successfully some problems, in particular in control of linear systems, but it has encountered di.culties in control of systems with high non-linearity. These were partially solved by the developing non-linear control theory and by adaptive control, but this efort has brought much more complex questions without a clear trend to their satisfactory solutions. We bring arguments that in some sense the same happened to fuzzy control a few decades later.

The third reason is a disillusion from the limits of computational power. At the first moment, people were fascinated by the newly open possibility of cheap high-precision computations ofered by computers. However, they recognized soon that some solutions are far from satisfactory. Simplified models failed to describe important features of real systems and the solutions did not perform well on some real-world systems.

Then it was found out that supreme precision is not as important. Instead of that, we need to describe (at least roughly) the complexity of the surrounding world. This requires a representation of numerous relations which are not precisely known, but whose effect is at least intuitively understood by humans. Fuzzy logic offered a tool allowing to implement these ideas easily.