As a hybrid intelligent system of soft computing technique, the fuzzy neural
network (FNN) is an efficient tool to deal with nonlinearly complicated
systems, in which there are linguistic information and data information, simultaneously.
In view of two basic problems—learning algorithm and universal
approximation, FNN's are thoroughly and systematically studied in the book.
The achievements obtained here are applied successfully to pattern recognition,
system modeling and identification, system forecasting, and digital image
restoration and so on. Many efficient methods and techniques to treat these
practical problems are developed.
As two main research objects, learning algorithms and universal approximations
of FNN's constitute the central part of the book. The basic tools to
study learning algorithms are the max-min (V — A) functions, the cuts of fuzzy
sets and interval arithmetic, etc. And the bridges to research universal approximations
of fuzzified neural networks and fuzzy inference type networks, such
as regular FNN's, polygonal FNN's, generalized fuzzy systems and generalized
fuzzy inference networks and so on are the fuzzy valued Bernstein polynomial,
the improved type extension principle and the piecewise linear functions. The
achievements of the book will provide us with the necessary theoretic basis for
soft computing technique and the applications of FNN's.