The purpose of this book is to provide the reader who is interested in
applications of fuzzy set theory, in the first place with a text to
which he or she can refer for the basic theoretical ideas, concepts and
techniques in this field and in the second place with a vast and up to
date account of the literature. Although there are now many books about
fuzzy set theory, and mainly about its applications, e. g. in control
theory, there is not really a book available which introduces the
elementary theory of fuzzy sets, in what I would like to call "a good
degree of generality". To write a book which would treat the entire
range of results concerning the basic theoretical concepts in great
detail and which would also deal with all possible variants and
alternatives of the theory, such as e. g. rough sets and L-fuzzy sets
for arbitrary lattices L, with the possibility-probability theories and
interpretations, with the foundation of fuzzy set theory via
multi-valued logic or via categorical methods and so on, would have been
an altogether different project. This book is far more modest in its
mathematical content and in its scope.
