1st Edition

# Fuzzy Sets & their Application to Clustering & Training

666 Pages
by CRC Press

664 Pages
by CRC Press

Also available as eBook on:

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