Introduction to Neuro-Fuzzy Systems Book

1	Fuzzy systems	1
1.1	An introduction to fuzzy logic	1
1.2	Operations on fuzzy sets	11
1.3	Fuzzy relations	18
1.4	The extension principle	26
1.5	The extension principle for n-place functions	29
1.6	Metrics for fuzzy numbers	39
1.7	Measures of possibility and necessity	41
1.8	Fuzzy implications	45
1.9	Linguistic variables	49
1.9.1	The linguistic variable Truth	50
1.10	The theory of approximate reasoning	53
1.11	An introduction to fuzzy logic controllers	71
1.12	Defuzzification methods	78
1.13	Inference mechanisms	81
1.14	Construction of data base and rule base of FLC	86
1.15	The ball and beam problem	91
1.16	Aggregation in fuzzy system modeling	95
1.17	Averaging operators	98
1.18	Fuzzy screening systems	109
1.19	Applications of fuzzy systems	115
	Bibliography	119
2	Artificial neural networks	133
2.1	The perceptron learning rule	133
2.2	The delta learning rule	143
2.3	The delta learning rule with semilinear activation function	149
2.4	The generalized delta learning rule	154
2.5	Affectivity of neural networks	157
2.6	Winner-take-all learning	160
2.7	Applications of artificial neural networks	164
	Bibliography	169
3	Fuzzy neural networks	171
3.1	Integration of fuzzy logic and neural networks	171
3.2	Fuzzy neurons	175
3.3	Hybrid neural nets	184
3.4	Computation of fuzzy logic inferences by hybrid neural net	195
3.5	Trainable neural nets for fuzzy IF-THEN rules	201
3.6	Implementation of fuzzy rules by regular FNN of Type 2	208
3.7	Implementation of fuzzy rules by regular FNN of Type 3	212
3.8	Tuning fuzzy control parameters by neural nets	216
3.9	Fuzzy rule extraction from numerical data	224
3.10	Neuro-fuzzy classifiers	228
3.11	FULLINS	235
3.12	Applications of fuzzy neural systems	240
	Bibliography	245
4	Appendix	255
4.1	Case study: A portfolio problem	255
4.1.1	Tuning the membership functions	259
4.2	Exercises	262
	Index	287