Fuzzy and Neuro-Fuzzy Intelligent Systems

by Czogala, Ernest; Leski, Jacek; CZOGAA, ERNEST; ESKI, JACEK

• ISBN13: 9783790812893
• ISBN10: 3790812897
• Edition: 1st
• Format: Hardcover
• Copyright: 2000-05-01
• Publisher: Springer-Verlag New York Inc

Summary

Provides an introduction to basic concepts as well as some advancements in fuzzy set theory, approximate reasoning, artificial neural networks, and clustering methods.

Table of Contents

Preface	vii
Classical sets and fuzzy sets Basic definitions and terminology	1	(26)
E. Czogala
J. Leski
Classical sets	1	(2)
Fuzzy sets	3	(2)
Operations on fuzzy sets	5	(10)
Classification of t-norms and t-conorms	15	(2)
De Morgan triple and other properties of t- and s-norms	17	(2)
Parameterized t-, s-norms and negations	19	(2)
Fuzzy relations	21	(1)
Cylindrical extension and projection of fuzzy sets	22	(1)
Extension principle	23	(1)
Linguistic variable	24	(2)
Summary	26	(1)
Bibliography notes	26	(1)
Approximate reasoning	27	(38)
J. Leski
E. Czogala
Interpretation of fuzzy conditional statement	27	(2)
An approach to axiomatic definition of fuzzy implication	29	(3)
Compositional rule of inference	32	(6)
Fuzzy reasoning	38	(2)
Canonical fuzzy if-then rule	40	(3)
Aggregation operation	43	(2)
Approximate reasoning using a fuzzy rule base	45	(1)
Approximate reasoning with singletons	46	(1)
Fuzzifiers and defuzzifiers	47	(4)
Equivalence of approximate reasoning results using different interpretations of if-then rules	51	(2)
Numerical results	53	(10)
Summary	63	(2)
Bibliographical notes	64	(1)
Artificial neural networks	65	(28)
J. Leski
Introduction	65	(2)
Artificial neural networks topologies	67	(4)
Feedforward multilayer networks	67	(2)
Radial basis function networks	69	(1)
Recurrent networks	70	(1)
Learning in artificial neural networks	71	(1)
Back-propagation learning rule	72	(4)
Modifications of the classic back-propagation method	76	(2)
Optimization methods in neural networks learning	78	(4)
Networks with output linearly depending on parameters	82	(5)
Global optimization methods	87	(5)
Summary	92	(1)
Bibliographical notes	92	(1)
Unsupervised learning Clustering methods	93	(36)
J. Leski
Introduction	93	(1)
Self-organizing feature map	93	(4)
Vector quantization and learning vector quantization	97	(2)
An overview of clustering methods	99	(8)
Hierarchical clustering	101	(1)
Graph theoretic clustering	102	(1)
Decomposition of density function	103	(2)
Clustering by minimizing criterion function	105	(2)
Fuzzy clustering methods	107	(6)
A possibilistic approach to clustering	113	(5)
New generalized weighted conditional fuzzy c-means	118	(2)
Fuzzy learning vector quantization	120	(3)
Cluster validity	123	(3)
Summary	126	(3)
Bibliographical notes	127	(2)
Fuzzy systems	129	(12)
J. Leski
E. Czogala
Introduction	129	(1)
The Mamdani fuzzy systems	130	(1)
The Takagi-Sugeno-Kang fuzzy systems	131	(2)
Fuzzy systems with parameterized consequents	133	(6)
Summary	139	(2)
Bibliographical notes	139	(2)
Neuro-fuzzy systems	141	(22)
J. Leski
E. Czogala
Introduction	141	(3)
Artificial neural network based fuzzy inference system	144	(6)
Classifier based on neuro-fuzzy system	150	(2)
ANNBFIS optimization using deterministic annealing	152	(2)
Further investigations of neuro-fuzzy systems	154	(9)
Summary	154	(1)
Bibliographical notes	155	(1)
Artificial neural network based fuzzy inference system-a MATLAB implementation	156	(5)
Proof of classifier learning convergence	161	(2)
Applications of artificial neural network based fuzzy inference system	163	(18)
J. Leski
E. Czogala
Introduction	163	(1)
Application to chaotic time series prediction	163	(3)
Application to ECG signal compression	166	(1)
Application to Ripley's synthetic two-class data classification	167	(3)
Application to the recognition of diabetes in Pima Indians	170	(1)
Application to the iris problem	171	(1)
Application to Monk's problems	171	(2)
Application to system identification	173	(2)
Application to control	175	(2)
Application to channel equalization	177	(2)
Summary	179	(2)
Biographical notes	180	(1)
References	181	(10)
List of notations and abbreviations	191