part I Basic aspects of fuzzy set theory -- chapter 1 Fuzzy Sets -- chapter 2 Properties of fuzzy set operations. Disjointness and fuzzy partitions -- chapter 3 Algebraic properties of the families of fuzzy sets -- chapter 4 Metric concepts for fuzzy sets -- chapter 5 Entropy and informational energy of finite fuzzy partitions -- chapter 6 Fuzziness and nonfuzziness measures -- part II Supervised fuzzy learning classifiers -- chapter 7 Fuzzy neural classifiers. Fuzzy perceptron algorithm and some relatives -- chapter 8 Fuzzy learning algorithms using squared criterion function -- part III One-level fuzzy partitional prototype-based clustering -- chapter 9 One-level clustering. Cluster substructure of a fuzzy class -- chapter 10 Other one-level clustering methods -- chapter 11 Linear cluster detection -- chapter 12 Adaptive algorithms for one-level fuzzy clustering -- chapter 13 Advanced adaptive algorithms -- chapter 14 Cluster validity -- chapter 15 Advanced cluster validity functionals -- chapter 16 Convergence of fuzzy clustering algorithms -- part IV Fuzzy discriminant analysis and hierarchical fuzzy clustering -- chapter 17 Fuzzy discriminant analysis and related clustering criteria -- chapter 18 Fuzzy hierarchical clustering -- chapter 19 Fuzzy simultaneous clustering.

"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."--Provided by publisher.