Bringing together the two seemingly unrelated concepts, fuzzy logic
andchaos theory, isprimarilymotivatedbytheconceptofsoft computing (SC),
initiated by Lot? A. Zadeh, the founder of fuzzy set theory. The
principal constituents of SC are fuzzy logic (FL), neural network theory
(NN) and probabilistic reasoning (PR), with the latter subsuming parts
of belief networks, genetic algorithms, chaos theory and learning
theory. What is important to note is that SC is not a melange of FL, NN
and PR. Rather, it is an integration in which each of the partners
contributes a distinct methodology for addressing problems in their
common domain. In this perspective, the principal cont- butions of FL,
NN and PR are complementary rather than competitive. SC di?ers from
conventional (hard) computing in that it is tolerant of imprecision,
uncertainty and partial truth. In e?ect, the role model for soft
computing is the human mind. From the general SC concept, we extract FL
and chaos theory as the object of this book to study their relationships
or interactions. Over the past few decades, fuzzy systems technology and
chaos theory have received ever increasing research interests from,
respectively, systems and control engineers, theoretical and
experimental physicists, applied ma- ematicians, physiologists, and
other communities of researchers. Especially, as one of the emerging
information processing technologies, fuzzy systems technology has
achieved widespread applications around the globe in many
industriesandtechnical?elds, rangingfromcontrol, automation,
andarti?cial intelligence (AI) to image/signal processing and pattern
recognition. On the otherhand,
inengineeringsystemschaostheoryhasevolvedfrombeingsimply a curious
phenomenon to one with real, practical signi?cance and utili
