Introduction: The Real Contribution of Fuzzy Systems

Abstract

Fuzzy logic (FL) was invented in the sixties by a leading expert in control engineering who realized that control theory had become beautiful enough to carry on its development on its own, but that there was many real problems it could not solve. Most real complex system control problems involve man. Hence applying control theory to complex control problems may require a formal understanding of how a human operator understands his system, what his goals are, and how he proceeds when controlling it. It requires a dedicated tool for representing human-originated information in a flexible way. And this is where fuzzy logic enters the picture (Zadeh [28]). In a paper that can be considered as the origin of the fuzzy rule-based approach, Zadeh [31] claimed that systems analysis and control requires a trade-off between representations that are very precise and accurate, such as numerical ones stemming from numerical functions, differential equations and the like, and representations that are intelligible, meaningful to humans, hence summarized, possibly in linguistic terms. However these two kinds of representations are sort of antagonistic because the more precise and accurate a representation, the less understandable it is, and conversely. This is Zadeh’s principle of incompatibility, and it explains the particular position of fuzzy logic in control and systems engineering, and the misunderstandings and controversies it has created in the control engineering community. The contribution of fuzzy systems may not be at the level where traditional systems engineers expect contributions: where they expect improved performance, they might get improved intelligibility, flexibility and transparency in the representation of dynamic systems and the design of controllers.