Fuzzy Sets & their Application to Clustering & Training

by Lazzerini; Beatrice

• ISBN13: 9780849305894
• ISBN10: 0849305896
• Edition: 1st
• Format: Hardcover
• Copyright: 2000-03-24
• Publisher: CRC Press

Summary

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.

Table of Contents

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