A general difficulty that arises when one tries to construct a model is that considerable idealizations are often necessary to move from a given problem to a suitable model. Although advances in computer technology have made it possible, in principle, to manage systems that are more and more complex, this has led at the same time to constantly growing conceptual demands to keep large software packages understandable. In the same way, large databases lose their applicability if their users are no longer in a position to extract the relevant information in a sensible way, and to have it presented in a proper form.

The research field of fuzzy theory originated from the need to simplify complex systems by tolerating a reasonable amount of imprecision, vagueness, and uncertainty during the modeling phase, yielding systems that are distorted to some extent, but, in many cases, capable of solving the modeling problem in an appropriate way. The primary goal of this monograph is to provide a unified and robust framework for the development of a broad class of applications in the areas of pattern recognition and image processing, in terms of fuzzy concepts and tools. The content is structured into five chapters.

Pattern recognition topics are discussed in chapter 1. Clustering with objective function models, using object data stated in terms of crisp, fuzzy, and possibilistic c-means models, is the topic addressed in chapter 2. Algorithms to optimize these models, methods that attempt to validate volumetric and shell-type clusters, and several versions of well-known statistical indices of validity are also presented here.

Two types of relational clustering--methods using decompositions of relation matrices, and methods relying on the optimization of an objective function of the relational data and fuzzy models using object data for classifier design--are presented in the next two chapters. Chapter 4 presents several models and algorithms inspired by neural-like networks, implemented mainly on a feed-forward multilayered perceptron trained by a back propagation learning algorithm; generalizations of adaptive resonance theory (ART); and radial basis function networks. Chapter 5 is entirely devoted to image processing and computer vision. Low-level vision approaches to image enhancement, as well as edge detection, image segmentation, boundary description, and surface approximation models, are presented here, together with a series of representative examples.

The content of the book is outstanding in terms of the clarity of the discourse and the variety of well-selected examples. The enlightening comments provided by the authors at the end of each chapter and the suggestions for further reading are also important features of the book.

The book supplies a comprehensive and sound presentation of some of the most significant applications of fuzzy algorithms for solving pattern recognition tasks. The exposition is concise, yet reader friendly. The concepts and methods are presented in a very clear and accessible way, and the illuminative examples provided by the authors are welcome, and enhance the pedagogical value of the text. This monograph will provide students, researchers, and application developers with the knowledge and tools needed to get the most out of the theory of using fuzzy sets and fuzzy systems for solving a large variety of cluster analysis and pattern recognition problems.