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 two research programs within FL, known as fuzzy logic in the narrow sense (FLN) and fuzzy logic in the broad sense (FLB), whose agendas are very different. The agenda of FLN is the development of propositional, predicate, and other fuzzy-logic calculi that are sound and complete in a similar sense as in classical logic. The agenda of FLB is to explore the rejection of the rigid principle of bivalence for emulating commonsense human reasoning in natural language and other unique capabilities of human beings. The book also examines principles for developing mathematics based on fuzzy logic and surveys established and prospective applications of fuzzy logic and mathematics based on fuzzy logic in various areas of human affairs. The principal aim of the book is to assess the significance of FL for these various areas and, especially, for mathematics. For this purpose, the well-known notion of paradigm shifts in science and its more recently discussed counterparts in mathematics and other areas, such as engineering or medicine, are employed.
Industry Reviews
"While the book certainly contains a very comprehensive and thoughtfully organized, up-to-date overview over almost all research areas connected to fuzzy logic that subscribe to a mathematical methodology, it also provides a highly informative and very balanced account of the debates and controversies that accompanied its history. ... it is not only invariably informative, but also a pleasure to read: central actors come to life and important events are
reviewed in a vivid manner. Moreover, even technical material is presented in an accessible style. ... the book will certainly remain an invaluable resource for more than one class of readers for quite some
time." -- Christian Fermüller, Notre Dame Philosophical Reviews
"Now this book has appeared, there is much that ensures that it will be the classic reference for many years to come. First, the book is rather complete... second, the book covers the history of the field... third, the scientific level is highly adequate." --Alfred Stein, Nieuw Archief voor Wiskunde
