The fuzzy set was conceived as a result of an attempt to come to grips with the problem of pattern recognition in the context of imprecisely defined categories. In such cases, the belonging of an object to a class is a matter of degree, as is the question of whether or not a group of objects form a cluster. A pioneering application of the theory of fuzzy sets to cluster analysis was made in 1969 by Ruspini. It was not until 1973, however, when the appearance of the work by Dunn and Bezdek on the Fuzzy ISODATA (or fuzzy c-means) algorithms became a landmark in the theory of cluster analysis, that the relevance of the theory of fuzzy sets to cluster analysis and pattern recognition became clearly established. Since then, the theory of fuzzy clustering has developed rapidly and fruitfully, with the author of the present monograph contributing a major share of what we know today. In their seminal work, Bezdek and Dunn have introduced the basic idea of determining the fuzzy clusters by minimizing an appropriately defined functional, and have derived iterative algorithms for computing the membership functions for the clusters in question. The important issue of convergence of such algorithms has become much better understood as a result of recent work which is described in the monograph.

Fuzzy Models and Algorithms for Pattern Recognition and Image Processing presents a comprehensive introduction of the use of fuzzy models in pattern recognition and selected topics in image processing and computer vision. Unique to this volume in the Kluwer Handbooks of Fuzzy Sets Series is the fact that this book was written in its entirety by its four authors. A single notation, presentation style, and purpose are used throughout. The result is an extensive unified treatment of many fuzzy models for pattern recognition. The main topics are clustering and classifier design, with extensive material on feature analysis relational clustering, image processing and computer vision. Also included are numerous figures, images and numerical examples that illustrate the use of various models involving applications in medicine, character and word recognition, remote sensing, military image analysis, and industrial engineering.

Contents:Introduction:Basic Concepts of Fuzzy SetsFuzzy RelationsFuzzy Models for Image Processing and Pattern RecognitionMembership Functions:IntroductionHeuristic SelectionsClustering ApproachesTuning of Membership FunctionsConcluding RemarksOptimal Image Thresholding:IntroductionThreshold Selection Based on Statistical Decision TheoryNon-fuzzy Thresholding AlgorithmsFuzzy Thresholding AlgorithmUnified Formulation of Three Thresholding AlgorithmsMultilevel ThresholdingApplicationsConcluding RemarksFuzzy Clustering:IntroductionC-Means AlgorithmFuzzy C-Means AlgorithmComparison between Hard and Fuzzy Clustering AlgorithmsCluster ValidityApplicationsConcluding RemarksLine Pattern Matching:IntroductionSimilarity Measures between Line SegmentsBasic Matching AlgorithmDealing with Noisy PatternsDealing with Rotated PatternsApplicationsConcluding RemarksFuzzy Rule-based Systems:IntroductionLearning from ExamplesDecision Tree ApproachFuzzy Aggregation Network ApproachMinimization of Fuzzy RulesDefuzzification and OptimizationApplicationsConcluding RemarksCombined Classifiers:IntroductionVoting SchemesMaximum Posteriori ProbabilityMultilayer Perceptron ApproachFuzzy Measures and Fuzzy IntegralsApplicationsConcluding Remarks Readership: Engineers and computer scientists. keywords:

This book constitutes the refereed proceedings of the Second International Symposium on Intelligent Data Analysis, IDA-97, held in London, UK, in August 1997. The volume presents 50 revised full papers selected from a total of 107 submissions. Also included is a keynote, Intelligent Data Analysis: Issues and Opportunities, by David J. Hand. The papers are organized in sections on exploratory data analysis, preprocessing and tools; classification and feature selection; medical applications; soft computing; knowledge discovery and data mining; estimation and clustering; data quality; qualitative models.

Fuzzy set theory - and its underlying fuzzy logic - represents one of the most significant scientific and cultural paradigms to emerge in the last half-century. Its theoretical and technological promise is vast, and we are only beginning to experience its potential. Clustering is the first and most basic application of fuzzy set theory, but forms the basis of many, more sophisticated, intelligent computational models, particularly in pattern recognition, data mining, adaptive and hierarchical clustering, and classifier design. Fuzzy Sets and their Application to Clustering and Training offers a comprehensive introduction to fuzzy set theory, focusing on the concepts and results needed for training and clustering applications. It provides a unified mathematical framework for fuzzy classification and clustering, a methodology for developing training and classification methods, and a general method for obtaining a variety of fuzzy clustering algorithms. The authors - top experts from around the world - combine their talents to lay a solid foundation for applications of this powerful tool, from the basic concepts and mathematics through the study of various algorithms, to validity functionals and hierarchical clustering. The result is Fuzzy Sets and their Application to Clustering and Training - an outstanding initiation into the world of fuzzy learning classifiers and fuzzy clustering.

Solving pattern recognition problems involves an enormous amount of computational effort. By applying genetic algorithms - a computational method based on the way chromosomes in DNA recombine - these problems are more efficiently and more accurately solved. Genetic Algorithms for Pattern Recognition covers a broad range of applications in science and technology, describing the integration of genetic algorithms in pattern recognition and machine learning problems to build intelligent recognition systems. The articles, written by leading experts from around the world, accomplish several objectives: they provide insight into the theory of genetic algorithms; they develop pattern recognition theory in light of genetic algorithms; and they illustrate applications in artificial neural networks and fuzzy logic. The cross-sectional view of current research presented in Genetic Algorithms for Pattern Recognition makes it a unique text, ideal for graduate students and researchers.