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.

Classification is the empirical process of creating a mapping from individual patterns to a set of classes and its subsequent use in predicting the classes to which new patterns belong. Tremendous energies have been expended in developing systems for the creation of the mapping component. Less effort has been devoted to the nature and analysis of the data component, namely, strategies that transform the data in order to simplify, in some sense, the classification process. The purpose of this thesis is to redress somewhat this imbalance by introducing two novel preprocessing methodologies. Fuzzy interruptible encoding determines the respective degrees to which a feature belongs to a collection of fuzzy sets and subsequently using these membership grades in place of the original feature. Burnishing tarnished gold standards compensates for the possible imprecision of a well-established reference test by adjusting, if necessary, the class labels in the design set while maintaining the test's vital discriminatory power. The methodologies were applied to several synthetic data sets as well as biomedical spectra acquired from magnetic resonance and infrared spectrometers. Both fuzzy encoding and burnishing consistently improved the discriminatory power of the underlying classifiers. They are insensitive to outliers and often reduce the training time for iterative classifiers such as the multi-layer perceptron. With the latter, reclassification only occurs for data within the design set; outliers within the test set are flagged but not altered. Therefore, the accepted gold standard is left in a pristine state sullied only by its original tarnish.

This book constitutes the refereed proceedings of the Third Mexican Conference on Pattern Recognition, MCPR 2011, held in Cancun, Mexico, in June/July 2011. The 37 revised full papers were carefully reviewed and selected from 69 submissions and are organized in topical sections on pattern recognition and data mining; computer vision and robotics; image processing; neural networks and signal processing; and natural language and document processing.

This book presents the complete philosophy of Fuzzy Set Theory. It offers a collection of views from scholars involved in various research projects concerning fuzziness in science, technology, economic systems, social sciences, logics and philosophy.