This book chiefly presents a novel approach referred to as backward fuzzy rule interpolation and extrapolation (BFRI). BFRI allows observations that directly relate to the conclusion to be inferred or interpolated from other antecedents and conclusions. Based on the scale and move transformation interpolation, this approach supports both interpolation and extrapolation, which involve multiple hierarchical intertwined fuzzy rules, each with multiple antecedents. As such, it offers a means of broadening the applications of fuzzy rule interpolation and fuzzy inference. The book deals with the general situation, in which there may be more than one antecedent value missing for a given problem. Two techniques, termed the parametric approach and feedback approach, are proposed in an attempt to perform backward interpolation with multiple missing antecedent values. In addition, to further enhance the versatility and potential of BFRI, the backward fuzzy interpolation method is extended to support a-cut based interpolation by employing a fuzzy interpolation mechanism for multi-dimensional input spaces (IMUL). Finally, from an integrated application analysis perspective, experimental studies based upon a real-world scenario of terrorism risk assessment are provided in order to demonstrate the potential and efficacy of the hierarchical fuzzy rule interpolation methodology.
|
|
|
1 | (16) |
|
|
|
2 | (5) |
|
|
|
2 | (2) |
|
1.1.2 Fuzzy Inference Systems |
|
|
4 | (3) |
|
1.2 The "Curse of Dimensionality" |
|
|
7 | (1) |
|
1.3 Fuzzy Rule Interpolation (FRI) |
|
|
8 | (1) |
|
1.4 Backward Fuzzy Rule Interpolation (BFRI) |
|
|
9 | (1) |
|
|
|
10 | (2) |
|
|
|
12 | (5) |
|
2 Background: Fuzzy Rule Interpolation |
|
|
17 | (42) |
|
2.1 General Properties of FRI Methods |
|
|
18 | (2) |
|
2.2 Categories of FRI Methods |
|
|
20 | (1) |
|
2.3 Single-Step Fuzzy Rule Interpolation Methods |
|
|
21 | (13) |
|
2.3.1 KH Interpolation Method |
|
|
21 | (5) |
|
2.3.2 Other Single-Step Fuzzy Rule Interpolation Methods |
|
|
26 | (8) |
|
2.4 Intermediate Rule-Based Fuzzy Interpolation Methods |
|
|
34 | (19) |
|
2.4.1 Scale and Move Transformation-Based FRI (T-FRI) |
|
|
35 | (9) |
|
2.4.2 Other Intermediate Rule-Based Interpolation Methods |
|
|
44 | (9) |
|
2.5 Comparison Based on General Properties |
|
|
53 | (1) |
|
|
|
54 | (1) |
|
|
|
54 | (5) |
|
3 Transformation-Based Backward Fuzzy Rule Interpolation with a Single Missing Antecedent Value |
|
|
59 | (16) |
|
3.1 General Concept of BFRI with Single Missing Antecedent Value |
|
|
61 | (1) |
|
|
|
62 | (3) |
|
3.2.1 Determination of the Closest Rules |
|
|
62 | (1) |
|
3.2.2 Construction of the Intermediate Fuzzy Terms |
|
|
63 | (1) |
|
3.2.3 Scale and Move Transformation |
|
|
64 | (1) |
|
|
|
65 | (7) |
|
|
|
72 | (1) |
|
|
|
73 | (2) |
|
4 Transformation Based Backward Fuzzy Rule Interpolation with Multiple Missing Antecedent Values |
|
|
75 | (16) |
|
|
|
75 | (4) |
|
|
|
79 | (3) |
|
|
|
82 | (6) |
|
|
|
88 | (1) |
|
|
|
88 | (3) |
|
5 An Alternative Backward Fuzzy Rule Interpolation Method |
|
|
91 | (16) |
|
5.1 Fuzzy Interpolation for Multidimensional Input Spaces |
|
|
91 | (9) |
|
|
|
94 | (3) |
|
|
|
97 | (3) |
|
5.2 Experimentation and Discussion |
|
|
100 | (6) |
|
5.2.1 Synthetic Evaluation |
|
|
100 | (1) |
|
|
|
101 | (5) |
|
|
|
106 | (1) |
|
|
|
106 | (1) |
|
6 Hierarchical Bidirectional Fuzzy Rule Interpolation and Rule Base Refinement |
|
|
107 | (14) |
|
6.1 Hierarchical Bidirectional Fuzzy Rule Interpolation |
|
|
108 | (3) |
|
6.1.1 Representation of Intermediate Variables |
|
|
108 | (1) |
|
|
|
109 | (1) |
|
|
|
110 | (1) |
|
6.2 Function Approximation and Experimental Evaluation |
|
|
111 | (3) |
|
|
|
111 | (2) |
|
6.2.2 Analysis of Results |
|
|
113 | (1) |
|
6.3 Refinement of Fuzzy Rule Base with HBFRI |
|
|
114 | (2) |
|
6.4 Numerical Example-Based Evaluation |
|
|
116 | (1) |
|
|
|
117 | (1) |
|
|
|
118 | (3) |
|
7 Application: Terrorism Risk Assessment Using BFRI |
|
|
121 | (22) |
|
|
|
121 | (3) |
|
7.2 A Hierarchical Terrorism Risk Assessment Framework |
|
|
124 | (5) |
|
7.2.1 Problem Specification |
|
|
124 | (1) |
|
|
|
124 | (5) |
|
7.3 Experimental Studies of TRA Using HBFRI |
|
|
129 | (9) |
|
7.3.1 Simulated Assessment of Terrorist Risk Using HBFRI |
|
|
129 | (3) |
|
7.3.2 Prediction and Decision Supporting for Local Government |
|
|
132 | (5) |
|
7.3.3 Practical Significance of BFRI |
|
|
137 | (1) |
|
7.3.4 Use of Alternative Distance Metrics |
|
|
137 | (1) |
|
7.3.5 Multiple Equally Probable Interpolative Outcomes |
|
|
138 | (1) |
|
|
|
138 | (1) |
|
|
|
139 | (4) |
|
|
|
143 | (10) |
|
|
|
143 | (3) |
|
8.1.1 Transformation Based S-BFRI |
|
|
143 | (1) |
|
8.1.2 Transformation Based M-BFRI |
|
|
144 | (1) |
|
8.1.3 An Alternative BFRI Method |
|
|
144 | (1) |
|
8.1.4 Refinement of Rule Base Based on HBFRI |
|
|
145 | (1) |
|
8.1.5 Application: Terrorism Risk Assessment |
|
|
145 | (1) |
|
|
|
146 | (3) |
|
8.2.1 Generalisation of BFRI |
|
|
146 | (1) |
|
8.2.2 BFRI Versus Fuzzy Inversion |
|
|
146 | (1) |
|
8.2.3 Antecedent And/Or Rule Selection in Interpolation |
|
|
147 | (1) |
|
8.2.4 Enhancement of M-BFRI |
|
|
147 | (1) |
|
8.2.5 Improve Hierarchical Interpolation Using BFRI |
|
|
147 | (1) |
|
8.2.6 BFRI Based Rule Base Refinement |
|
|
148 | (1) |
|
8.2.7 "Many-to-One" Problem in BFRI |
|
|
148 | (1) |
|
8.2.8 Further Applications of FRI/BFRI |
|
|
149 | (1) |
|
|
|
149 | (4) |
| Appendix A Glossary of Terms |
|
153 | (4) |
| Appendix B Examples for Calculations |
|
157 | |
Shangzhu Jin received his B.Sc. degree in Computer Science from Beijing Technology and Business University, China, his M.Sc. degree in Control Theory and Control from Yanshan University, China, and his Ph.D. degree from Aberystwyth University, UK. He is currently an Associate Professor at the School of Electronic Information Engineering, Chongqing University of Science and Technology. His research interests include fuzzy systems, approximate reasoning, and network security. His paper, entitled Backward Fuzzy Interpolation and Extrapolation with Multiple Multi-antecedent Rules won the best student paper award at the 21st IEEE International Conference on Fuzzy Systems.
Qiang Shen is a Professor and Director of the Institute of Mathematics, Physics and Computer Science (IMPACS) at Aberystwyth University. His major research interests include computational intelligence, fuzzy and qualitative systems, reasoning and learning under uncertainty, pattern recognition, data mining, and real-world applications of such techniques for decision support (e.g., crime detection, space exploration, consumer profiling, systems monitoring, and medical diagnosis). He has published two research monographs and over 360 peer-refereed papers. A number of his papers have received prestigious international prizes.
Jun Peng received a Ph.D. degree in Computer Software and Theory from Chongqing University in 2003, an M.A. in Computer System Architecture from Chongqing University in 2000, and a BSc in Applied Mathematics from Northeast University in 1992. From 1992 to present he has worked at Chongqing University of Science and Technology, where he is currently a Professor and Dean of the School of Electrical and Information Engineering. He was a visiting scholar in the Laboratory of Cryptography and Information Security at Tsukuba University, Japan in 2004, and at theDepartment of Computer Science at California State University, Sacramento in 2007, respectively. He has authored or coauthored over 60 peer-reviewed journal and conference papers. He has served as a program committee member or session co-chair for over 10 international conferences, e.g. the IEEE SEKE10, ICCI*CC11-17, ICISME 2012, andICOACS16. His current research interests are in cryptography, chaos and network security, image processingand intelligence computation.
Biežāk uzdotie jautājumi par e-grāmatām