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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.
List of contents
Fuzzy Sets. Entropy of Finite Fuzzy Partitions. Fuzziness and Non-Fuzziness Measures. Fuzzy Training Procedures. One-Level Classification: Cluster Substructure of a Fuzzy Class. One-Level Classification: Adaptive Algorithms. Cluster Validity. Convergence of Fuzzy clustering Algorithms. Fuzzy Discriminant Analysis and Related Clustering Criteria. Divisive Hierarchical Clustering. Classification with Structural Constraints. Classification in Pseudometric Spaces. Bibliography.
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About the author
Beatrice Lazzerini, Lakhmi C. Jain, D. Dumitrescu
Summary
Fuzzy logic applications allow uncertain or imprecise data to be clustered and analyzed when traditional methods cannot be used. This volume offers an introduction to fuzzy set theory and then progresses through the algorithms and techniques used to manipulate data using fuzzy sets, including classification, hierarchy, and cluster structure.
