Forward
The past few years have witnessed a rapid growth in the number and variety
of applications of fuzzy logic. The applications range from consumer products
such as cameras, camcorders, washing machines, and microwave ovens to
industrial process control, medical instrumentation, decision-support systems,
and portfolio selection.
To understand the reasons for the growing use of fuzzy logic it is necessary,
first, to clarify what is meant by fuzzy logic.
Fuzzy logic has two different meanings. In a narrow sense, fuzzy logic is a
logical system, which is an extension of multivalued logic. But in a wider
sense—which is in predominant use today—fuzzy logic (FL) is almost
synonymous with the theory of fuzzy sets, a theory which relates to classes of
objects with unsharp boundaries in which membership is a matter of degree.
In this perspective, fuzzy logic in its narrow sense is a branch of FL. What is
important to recognize is that, even in its narrow sense, the agenda of fuzzy
logic is very different both in spirit and substance from the agendas of
traditional multivalued logical systems.
In the Fuzzy Logic Toolbox, fuzzy logic should be interpreted as FL, that is,
fuzzy logic in its wide sense. The basic ideas underlying FL are explained very
clearly and insightfully in the Introduction. What might be added is that the
basic concept underlying FL is that of a linguistic variable, that is, a variable
whose values are words rather than numbers. In effect, much of FL may be
viewed as a methodology for computing with words rather than numbers.
Although words are inherently less precise than numbers, their use is closer to
human intuition. Furthermore, computing with words exploits the tolerance
for imprecision and thereby lowers the cost of solution.
Another basic concept in FL, which plays a central role in most of its
applications, is that of a fuzzy if-then rule or, simply, fuzzy rule. Although
rule-based systems have a long history of use in AI, what is missing in such
systems is a machinery for dealing with fuzzy consequents and/or fuzzy
antecedents. In fuzzy logic, this machinery is provided by what is called the
calculus of fuzzy rules. The calculus of fuzzy rules serves as a basis for what
might be called the Fuzzy Dependency and Command Language (FDCL).
Although FDCL is not used explicitly in Fuzzy Logic Toolbox, it is effectively
one of its principal constituents. In this connection, what is important to
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