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.