In the two decades since its inception by L. Zadeh, the theory of fuzzy
sets has matured into a wide-ranging collection of concepts, models, and
tech- niques for dealing with complex phenomena which do not lend
themselves to analysis by classical methods based on probability theory
and bivalent logic. Nevertheless, a question which is frequently raised
by the skeptics is: Are there, in fact, any significant problem areas in
which the use of the theory of fuzzy sets leads to results which could
not be obtained by classical methods? The approximately 5000
publications in this area, which are scattered over many areas such as
artificial intelligence, computer science, control engineering, decision
making, logic, operations research, pattern recognition, robotics and
others, provide an affirmative answer to this question. In spite of the
large number of publications, good and comprehensive textbooks which
could facilitate the access of newcomers to this area and support
teaching were missing until recently. To help to close this gap and to
provide a textbook for courses in fuzzy set theory which can also be
used as an introduction to this field, the first volume ofthis book was
published in 1985 [Zimmermann 1985 b]. This volume tried to cover
fuzzy set theory and its applications as extensively as possible.
Applications could, therefore, only be described to a limited extent and
not very detailed.