Complexity Management in Fuzzy Systems: A Rule Base Compression Approach

Front Cover
Springer, Jun 2, 2007 - Science - 349 pages
Doing research is a great adventure As any adventure sometimes it is hard You may feel alone and with no idea where to go But if you have courage and press onwards You will eventually stand where no one has stood And see the world as no one has seen it There can be no better feeling than this! Adaptation from ‘Introduction to Research’, Tom Addis (2004) The idea about this book has been on the author’s mind for almost a decade but it was only about a couple of years ago when the underlying research process was actually started. The reason for this delay has been the insufficient spare time for research being a lecturer in a ‘new’ UK university where the emphasis is mainly on teaching. And maybe this book would have never been written if the author had not been presented with the chance of developing new teaching modules in fuzzy logic that have given him food for thought in a research related context and have helped him combine efficiently his teaching and research activities. The title of this book may sound too specialised but it has a much wider meaning. Fuzzy systems are any systems for modelling, simulation, control, prediction, diagnosis, decision making, pattern recognition, image processing, etc. which use fuzzy logic. Although fuzzy logic is an advanced extension of binary logic, the latter is still used predominantly today.
 

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Contents

62 Manipulation with Identity Rule Bases
119
63 Manipulation with Transpose Rule Bases
127
64 Manipulation with Permutation Rule Bases
138
65 Specific Cases with Special Rule Bases
144
66 Analysis of Manipulation Techniques with Special Rule Bases
150
Formal Transformation of Fuzzy Rule Based Systems
152
73 Combined Merging Manipulations
158
74 Self Standing Inputs and Outputs
164

23 Multiple Output and Single Output Systems
10
24 Feedforward and Feedback Systems
11
25 Single Rule Base and Multiple Rule Base Systems
12
26 Complexity Analysis in Fuzzy Systems
14
Rule Base Reduction Methods for Fuzzy Systems
17
32 Removal and Fusion of Inputs
19
33 Singular Value Decomposition of Output Matrix
21
34 Conversion into Union Rule Configuration
23
35 Spatial Decomposition into Subsystems
25
36 Decomposition into Multilayer Hierarchical Structure
26
37 Comparative Analysis of Reduction Methods
29
Formal Presentation of Fuzzy Rule Based Systems
32
42 Analysis of Rule Base Properties
36
43 Presentation of Rule Bases by Boolean Matrices
39
44 Presentation of Rule Bases by Binary Relations
46
45 Comparative Analysis of Formal Presentation Techniques
53
46 Application Range of Formal Presentation Techniques
55
Formal Manipulation of Fuzzy Rule Based Systems
65
53 Vertical Splitting Manipulation of Rule Bases
73
54 Horizontal Merging Manipulation of Rule Bases
81
55 Horizontal Splitting Manipulation of Rule Bases
87
56 Output Merging Manipulation of Rule Bases
92
57 Output Splitting Manipulation of Rule Bases
102
58 Comparative Analysis of Formal Manipulation Techniques
112
59 Application Range of Formal Manipulation Techniques
113
Formal Manipulation with Special Rule Bases
115
75 Total and Partial Identity Lines
173
76 Comparative Analysis of Formal Transformation Techniques
181
77 Application Range of Formal Transformation Techniques
182
Formal Transformation of Feedback Rule Bases
185
83 Transformation of Rule Bases with Local Feedback
190
84 Transformation of Rule Bases with Global Feedback
201
85 Transformation of Rule Bases with Nested Feedback
211
86 Transformation of Rule Bases with Overlapping Feedback
226
87 Transformation of Rule Bases with Crossed Feedback
234
88 Transformation of Rule Bases with Multiple Feedback
249
89 Feedback Rule Base Design
257
810 Canonical Rule Base Networks
264
811 Analysis of Transformation Techniques for Feedback Rule Bases
268
Formal Simplification of Fuzzy Rule Based Systems
269
92 Rule Base Simplification by Aggregation of Inconsistent Rules
274
93 Rule Base Simplification by Filtration of Nonmonotonic Rules
287
94 Complexity Evaluation of Formal Simplification Techniques
328
95 Comparative Analysis of Formal Simplification Techniques
338
96 Application Range of Formal Simplification Techniques
339
Conclusion
341
103 Application Framework for Fuzzy Rule Base Compression
342
104 Future Directions for Related Research in Fuzzy Systems
343
105 Overall Book Evaluation
344
References
345
Index
349
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