Foreword |
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xiii | |
Preface |
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xv | |
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1 Clustering and Fuzzy Clustering |
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1 | (27) |
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1 | (1) |
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1.2 Basic Notions and Notation |
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1 | (5) |
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2 | (1) |
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1.2.2 Distance and Similarity |
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2 | (4) |
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1.3 Main Categories of Clustering Algorithms |
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6 | (4) |
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1.3.1 Hierarchical Clustering |
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6 | (2) |
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1.3.2 Objective Function-Based Clustering |
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8 | (2) |
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1.4 Clustering and Classification |
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10 | (1) |
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11 | (7) |
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18 | (1) |
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1.7 Extensions of Objective Function-Based Fuzzy Clustering |
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19 | (4) |
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1.7.1 Augmented Geometry of Fuzzy Clusters: Fuzzy C Varieties |
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19 | (1) |
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1.7.2 Possibilistic Clustering |
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20 | (2) |
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22 | (1) |
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1.8 Self-Organizing Maps and Fuzzy Objective Function-Based Clustering |
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23 | (2) |
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25 | (1) |
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26 | (2) |
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2 Computing with Granular Information: Fuzzy Sets and Fuzzy Relations |
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28 | (22) |
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2.1 A Paradigm of Granular Computing: Information Granules and Their Processing |
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28 | (3) |
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2.2 Fuzzy Sets as Human-Centric Information Granules |
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31 | (1) |
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2.3 Operations on Fuzzy Sets |
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32 | (1) |
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33 | (2) |
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2.5 Comparison of Two Fuzzy Sets |
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35 | (2) |
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2.6 Generalizations of Fuzzy Sets |
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37 | (1) |
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38 | (6) |
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44 | (2) |
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2.9 Granular Computing and Distributed Processing |
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46 | (1) |
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47 | (1) |
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47 | (3) |
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3 Logic-Oriented Neurocomputing |
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50 | (16) |
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50 | (1) |
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3.2 Main Categories of Fuzzy Neurons |
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51 | (8) |
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3.2.1 Aggregative Neurons |
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52 | (3) |
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3.2.2 Referential (Reference) Neurons |
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55 | (4) |
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3.3 Architectures of Logic Networks |
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59 | (2) |
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3.4 Interpretation Aspects of the Networks |
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61 | (1) |
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3.5 Granular Interfaces of Logic Processing |
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62 | (2) |
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64 | (1) |
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64 | (2) |
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4 Conditional Fuzzy Clustering |
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66 | (21) |
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66 | (2) |
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4.2 Problem Statement: Context Fuzzy Sets and Objective Function |
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68 | (2) |
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4.3 The Optimization Problem |
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70 | (10) |
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4.4 Computational Considerations of Conditional Clustering |
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80 | (1) |
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4.5 Generalizations of the Algorithm Through the Aggregation Operator |
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81 | (1) |
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4.6 Fuzzy Clustering with Spatial Constraints |
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82 | (4) |
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86 | (1) |
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86 | (1) |
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5 Clustering with Partial Supervision |
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87 | (10) |
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87 | (1) |
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88 | (2) |
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5.3 Design of the Clusters |
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90 | (1) |
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5.4 Experimental Examples |
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91 | (2) |
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5.5 Cluster-Based Tracking Problem |
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93 | (3) |
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96 | (1) |
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96 | (1) |
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6 Principles of Knowledge-Based Guidance in Fuzzy Clustering |
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97 | (32) |
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97 | (2) |
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6.2 Examples of Knowledge-Oriented Hints and Their General Taxonomy |
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99 | (3) |
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6.3 The Optimization Environment of Knowledge-Enhanced Clustering |
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102 | (3) |
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6.4 Quantification of Knowledge-Based Guidance Hints and Their Optimization |
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105 | (2) |
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6.5 Organization of the Interaction Process |
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107 | (5) |
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6.6 Proximity-Based Clustering (P-FCM) |
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112 | (5) |
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6.7 Web Exploration and P-FCM |
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117 | (9) |
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6.8 Linguistic Augmentation of Knowledge-Based Hints |
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126 | (1) |
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127 | (1) |
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127 | (2) |
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7 Collaborative Clustering |
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129 | (29) |
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7.1 Introduction and Rationale |
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129 | (2) |
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7.2 Horizontal and Vertical Clustering |
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131 | (1) |
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7.3 Horizontal Collaborative Clustering |
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132 | (8) |
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7.3.1 Optimization Details |
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135 | (2) |
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7.3.2 The Flow of Computing of Collaborative Clustering |
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137 | (1) |
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7.3.3 Quantification of the Collaborative Phenomenon of Clustering |
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138 | (2) |
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140 | (10) |
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7.5 Further Enhancements of Horizontal Clustering |
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150 | (1) |
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7.6 The Algorithm of Vertical Clustering |
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151 | (2) |
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7.7 A Grid Model of Horizontal and Vertical Clustering |
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153 | (2) |
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155 | (2) |
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157 | (1) |
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157 | (1) |
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158 | (20) |
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158 | (1) |
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159 | (4) |
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8.2.1 The Objective Function |
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160 | (1) |
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8.2.2 The Logic Transformation Between Information Granules |
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161 | (2) |
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163 | (3) |
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8.4 The Development Framework of Directional Clustering |
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166 | (1) |
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167 | (7) |
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174 | (2) |
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176 | (2) |
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9 Fuzzy Relational Clustering |
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178 | (13) |
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9.1 Introduction and Problem Statement |
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178 | (1) |
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9.2 FCM for Relational Data |
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179 | (2) |
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9.3 Decomposition of Fuzzy Relational Patterns |
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181 | (7) |
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9.3.1 Gradient-Based Solution to the Decomposition Problem |
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182 | (2) |
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9.3.2 Neural Network Model of the Decomposition Problem |
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184 | (4) |
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188 | (1) |
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189 | (1) |
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189 | (2) |
10 Fuzzy Clustering of Heterogeneous Patterns |
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191 | (18) |
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191 | (1) |
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192 | (2) |
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10.3 Parametric Models of Granular Data |
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194 | (1) |
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10.4 Parametric Mode of Heterogeneous Fuzzy Clustering |
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195 | (3) |
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10.5 Nonparametric Heterogeneous Clustering |
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198 | (9) |
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10.5.1 A Frame of Reference |
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198 | (2) |
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10.5.2 Representation of Granular Data Through the Possibility-Necessity Transformation |
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200 | (5) |
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205 | (2) |
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207 | (1) |
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208 | (1) |
11 Hyperbox Models of Granular Data: The Tchebyschev FCM |
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209 | (17) |
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209 | (1) |
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210 | (1) |
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11.3 The Clustering Algorithm Detailed Considerations |
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211 | (7) |
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11.4 Development of Granular Prototypes |
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218 | (2) |
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11.5 Geometry of Information Granules |
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220 | (3) |
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11.6 Granular Data Description: A General Model |
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223 | (1) |
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223 | (1) |
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224 | (2) |
12 Genetic Tolerance Fuzzy Neural Networks |
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226 | (20) |
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226 | (1) |
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12.2 Operations of Thresholding and Tolerance: Fuzzy Logic-Based Generalizations |
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227 | (4) |
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12.3 Topology of the Logic Network |
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231 | (4) |
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12.4 Genetic Optimization |
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235 | (1) |
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12.5 Illustrative Numeric Studies |
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236 | (8) |
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244 | (1) |
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245 | (1) |
13 Granular Prototyping |
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246 | (24) |
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246 | (1) |
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247 | (4) |
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13.2.1 Expressing Similarity Between Two Fuzzy Sets |
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247 | (1) |
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13.2.2 Performance Index (Objective Function) |
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248 | (3) |
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13.3 Prototype Optimization |
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251 | (12) |
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13.4 Development of Granular Prototypes |
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263 | (5) |
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13.4.1 Optimization of the Similarity Levels |
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263 | (1) |
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13.4.2 An Inverse Similarity Problem |
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264 | (4) |
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268 | (1) |
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268 | (2) |
14 Granular Mappings |
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270 | (13) |
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14.1 Introduction and Problem Statement |
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270 | (1) |
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14.2 Possibility and Necessity Measures as the Computational Vehicles of Granular Representation |
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271 | (1) |
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14.3 Building the Granular Mapping |
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272 | (3) |
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14.4 Designing Multivariable Granular Mappings Through Fuzzy Clustering |
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275 | (3) |
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14.5 Quantification of Granular Mappings |
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278 | (1) |
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14.6 Experimental Studies |
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278 | (2) |
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280 | (2) |
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282 | (1) |
15 Linguistic Modeling |
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283 | (14) |
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283 | (2) |
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15.2 Cluster-Based Representation of Input-Output Mapping |
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285 | (2) |
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15.3 Conditional Clustering in the Development of a Blueprint of Granular Models |
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287 | (3) |
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15.4 The Granular Neuron as a Generic Processing Element in Granular Networks |
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290 | (3) |
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15.5 The Architecture of Linguistic Models Based on Conditional Fuzzy Clustering |
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293 | (1) |
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15.6 Refinements of Linguistic Models |
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294 | (1) |
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295 | (1) |
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296 | (1) |
Bibliography |
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297 | (18) |
Index |
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315 | |