Introduction to Neuro-Fuzzy Systems

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Springer Science & Business Media, 2000 - Business & Economics - 289 pages
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Fuzzy sets were introduced by Zadeh (1965) as a means of representing and manipulating data that was not precise, but rather fuzzy. Fuzzy logic pro vides an inference morphology that enables approximate human reasoning capabilities to be applied to knowledge-based systems. The theory of fuzzy logic provides a mathematical strength to capture the uncertainties associ ated with human cognitive processes, such as thinking and reasoning. The conventional approaches to knowledge representation lack the means for rep resentating the meaning of fuzzy concepts. As a consequence, the approaches based on first order logic and classical probablity theory do not provide an appropriate conceptual framework for dealing with the representation of com monsense knowledge, since such knowledge is by its nature both lexically imprecise and noncategorical. The developement of fuzzy logic was motivated in large measure by the need for a conceptual framework which can address the issue of uncertainty and lexical imprecision. Some of the essential characteristics of fuzzy logic relate to the following [242]. • In fuzzy logic, exact reasoning is viewed as a limiting case of ap proximate reasoning. • In fuzzy logic, everything is a matter of degree. • In fuzzy logic, knowledge is interpreted a collection of elastic or, equivalently, fuzzy constraint on a collection of variables. • Inference is viewed as a process of propagation of elastic con straints. • Any logical system can be fuzzified. There are two main characteristics of fuzzy systems that give them better performance für specific applications.
 

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Contents

1 Fuzzy systems
1
12 Operations on fuzzy sets
11
13 Fuzzy relations
18
14 The extension principle
26
15 The extension principle for nplace functions
29
16 Metrics for fuzzy numbers
39
17 Measures of possibility and necessity
41
18 Fuzzy implications
45
24 The generalized delta learning rule
154
25 Effectivity of neural networks
157
26 Winnertakeall learning
160
27 Applications of artificial neural networks
164
Bibliography
169
3 Fuzzy neural networks
171
32 Fuzzy neurons
175
33 Hybrid neural nets
184

19 Linguistic variables
49
191 The linguistic variable Truth
50
110 The theory of approximate reasoning
53
111 An introduction to fuzzy logic controllers
71
112 Defuzzification methods
78
113 Inference mechanisms
81
114 Construction of data base and rule base of FLC
86
115 The ball and beam problem
91
116 Aggregation in fuzzy system modeling
95
117 Averaging operators
98
118 Fuzzy screening systems
109
119 Applications of fuzzy systems
115
Bibliography
119
2 Artificial neural networks
133
22 The delta learning rule
143
23 The delta learning rule with semilinear activation function
149
34 Computation of fuzzy logic inferences by hybrid neural net
195
35 Trainable neural nets for fuzzy IFTHEN rules
201
36 Implementation of fuzzy rules by regular FNN of Type 2
208
37 Implementation of fuzzy rules by regular FNN of Type 3
212
38 Tuning fuzzy control parameters by neural nets
216
39 Fuzzy rule extraction from numerical data
224
310 Neurofuzzy classifiers
228
311 FULLINS
235
312 Applications of fuzzy neural systems
240
Bibliography
245
4 Appendix
255
411 Tuning the membership functions
259
42 Exercises
262
Index
287
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About the author (2000)

Roy Fuller is a private consultant in intestinal microecology, operating from Reading, UK