This book presents a mathematically-based introduction into the
fascinating topic of Fuzzy Sets and Fuzzy Logic and might be used
as textbook at both undergraduate and graduate levels and also as
reference guide for mathematician, scientists or engineers who
would like to get an insight into Fuzzy Logic. Fuzzy Sets have been
introduced by Lotfi Zadeh in 1965 and since then, they have been
used in many applications. As a consequence, there is a vast
literature on the practical applications of fuzzy sets, while
theory has a more modest coverage. The main purpose of the present
book is to reduce this gap by providing a theoretical introduction
into Fuzzy Sets based on Mathematical Analysis and Approximation
Theory. Well-known applications, as for example fuzzy control, are
also discussed in this book and placed on new ground, a theoretical
foundation. Moreover, a few advanced chapters and several new
results are included. These comprise, among others, a new
systematic and constructive approach for fuzzy inference systems of
Mamdani and Takagi-Sugeno types, that investigates their
approximation capability by providing new error estimates.
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