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Fuzzy Logic and Mathematics - A Historical Perspective (Hardcover)
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Fuzzy Logic and Mathematics - A Historical Perspective (Hardcover)
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The term "fuzzy logic" (FL), as it is understood in this book,
stands for all aspects of representing and manipulating knowledge
based on the rejection of the most fundamental principle of
classical logic: the principle of bivalence. According to this
principle, each declarative sentence is required to be either true
or false. In fuzzy logic, these classical truth values are not
abandoned. However, additional, intermediary truth values between
true and false are allowed, which are interpreted as degrees of
truth. This opens a new way of thinking-thinking in terms of
degrees rather than absolutes. For example, it led to the
definition of a new category of sets, referred to as fuzzy sets, in
which membership is a matter of degree. The book examines the
genesis and development of fuzzy logic. It surveys the prehistory
of fuzzy logic and inspects circumstances that eventually lead to
the emergence of fuzzy logic. The book explores in detail the
development of propositional, predicate, and other calculi that
admit degrees of truth, which are known as fuzzy logic in the
narrow sense. Fuzzy logic in the broad sense, whose primary aim is
to utilize degrees of truth for emulating common-sense human
reasoning in natural language, is scrutinized as well. The book
also examines principles for developing mathematics based on fuzzy
logic and provides overviews of areas in which this has been done
most effectively. It also presents a detailed survey of established
and prospective applications of fuzzy logic in various areas of
human affairs, and provides an assessment of the significance of
fuzzy logic as a new paradigm.
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