My 1965 paper on fuzzy sets was motivated in large measure by the conviction that traditional methods of systems analysis are unsuited for dealing with systems in which relations between variables do not lend themselves to representation in terms of differential or difference equations. Such systems are the norm in biology, sociology, economics and, more generally, in fields in which the systems are humanistic rather than mechanistic in nature.
Traditional methods of analysis are oriented toward the use of numerical techniques. By contrast, much of human reasoning involves the use of variables whose values are fuzzy sets. This observation is the basis for the concept of a linguistic variable, that is, a variable whose values are words rather than numbers. The concept of a linguistic variable has played and is continuing to play a key role in the applications of fuzzy set theory and fuzzy logic.
The use of linguistic variables represents a significant paradigm shift in systems analysis. More specifically, in the linguistic approach the focus of attention in the representation of dependencies shifts from difference and differential equations to fuzzy if-then rules in the form if X is A then Y is B, where X and Y are linguistic variables and A and B are their linguistic values, e.g., if Pressure is high then Volume is low. Such rules serve to characterize imprecise dependencies and constitute the point of departure for the construction of what might be called the calculus of fuzzy rules or CFR, for short. In this perspective, The Fuzzy Systems Handbook may be viewed as an up-to-date, informative and easy-to-follow introduction to the methodology of fuzzy if-then rules and its applications. A key aspect of this methodology is that its role model is the human mind.