1st Edition

Fuzzy Sets & their Application to Clustering & Training

    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.

    BASIC ASPECTS OF FUZZY SET THEORY
    Fuzzy Sets
    Properties of Fuzzy Set Operations. Disjointness and Fuzzy Partitions
    Algebraic Properties of the Families of Fuzzy Sets
    Metric Concepts for Fuzzy Sets
    Entropy and Informational Energy of Finite Fuzzy Partitions
    Fuzziness and Nonfuzziness Measures
    SUPERVISED FUZZY LEARNING CLASSIFIERS
    Fuzzy Neural Classifiers. Fuzzy Perceptron Algorithm and some Relatives
    Fuzzy Learning Algorithms using Squared Criterion Function
    ONE-LEVEL FUZZY PARTITIONAL PROTOTYPE-BASED CLUSTERING
    One Level Clustering. Cluster Substructure of a Fuzzy Class
    Other One-Level Clustering Methods
    Linear Cluster Detection
    Adaptive Algorithms for One-Level Fuzzy Clustering
    Advanced Adaptive Algorithms
    Cluster Validity
    Advanced Cluster Validity Functionals
    Convergence of Fuzzy Clustering Algorithms
    FUZZY DISCRIMINANT ANALYSIS AND HIERARCHICAL FUZZY CLUSTERING
    Fuzzy Discriminant Analysis and Related Clustering Criteria
    Fuzzy Hierarchical Clustering
    Fuzzy Simultaneous Clustering
    INDEX

    Biography

    Beatrice Lazzerini, Lakhmi C. Jain, D. Dumitrescu