| Note to the Reader | p. V |
| Foreword | p. IX |
| Preface | p. XI |
| p. 1 |
| Knowledge Discovery | p. 3 |
| Knowledge Discovery Background and History | p. 5 |
| The Knowledge Discovery Process | p. 6 |
| A simple illustrative example problem | p. 6 |
| Knowledge discovery | p. 6 |
| Successes of Knowledge Discovery | p. 12 |
| Cartesian Granules Features in Brief | p. 13 |
| Soft computing for knowledge discovery | p. 13 |
| The Structure of This Book | p. 14 |
| Summary | p. 17 |
| Bibliography | p. 17 |
| p. 21 |
| Knowledge Representation | p. 23 |
| Representation of Observations and Hypotheses | p. 24 |
| General Purpose Knowledge--Inference and Decision Making | p. 25 |
| Uncertainty and Knowledge Representation | p. 25 |
| Desiderata of Knowledge Representation | p. 26 |
| A Taxonomy of Knowledge Representation | p. 27 |
| Symbolic-based approaches | p. 28 |
| Probability-based approaches | p. 28 |
| Fuzzy-based approaches | p. 29 |
| Mathematical-based approaches | p. 30 |
| Prototype-based approaches | p. 31 |
| Summary | p. 32 |
| Bibliography | p. 32 |
| Fuzzy Set Theory | p. 35 |
| Classical Set Theory | p. 35 |
| Fuzzy Set Theory | p. 37 |
| Motivations | p. 37 |
| Fuzzy sets | p. 38 |
| Notation convention | p. 40 |
| Interpretations of fuzzy sets | p. 41 |
| Properties of fuzzy sets | p. 43 |
| Representation of fuzzy sets | p. 45 |
| Fuzzy set operations | p. 47 |
| Axiomatic-based operators - t-norms and t-conorms | p. 50 |
| Averaging operators | p. 54 |
| Compensative operators | p. 55 |
| Matching fuzzy sets | p. 56 |
| Generalisations of fuzzy sets | p. 57 |
| Multi dimensional fuzzy sets | p. 57 |
| Cartesian granule fuzzy sets | p. 61 |
| Higher order fuzzy sets | p. 61 |
| Choosing membership functions | p. 63 |
| Summary | p. 64 |
| Bibliography | p. 64 |
| Fuzzy Logic | p. 67 |
| Fuzzy rules and facts | p. 67 |
| Linguistic partitions, variables and hedges | p. 69 |
| Linguistic hedges | p. 76 |
| Fuzzy Inference | p. 76 |
| Compositional rule of inference (CRI) | p. 77 |
| Fuzzy decision making for prediction - defuzzification | p. 85 |
| Centre of gravity (COG) method | p. 86 |
| Maximum height method | p. 87 |
| Fuzzy decision making for classification | p. 87 |
| Applications of fuzzy logic | p. 89 |
| Summary | p. 89 |
| Bibliography | p. 89 |
| Probability Theory | p. 93 |
| Fundamentals of probability theory | p. 94 |
| Point-based probability theory | p. 97 |
| Joint probability distributions | p. 97 |
| Naive Bayes | p. 98 |
| Bayesian networks | p. 99 |
| Set-based probability theory | p. 102 |
| Dempster-Shafter theory | p. 103 |
| Possibility theory | p. 109 |
| Mass assignment theory | p. 113 |
| From fuzzy sets to probability distributions | p. 118 |
| Transforming fuzzy sets into probability distributions | p. 119 |
| From memberships to probabilities - a voting model justification | p. 123 |
| Zadeh's probability of fuzzy events | p. 124 |
| Summary | p. 125 |
| Bibliography | p. 126 |
| Fril - A Support Logic Programming Environment | p. 129 |
| Fril rules and facts | p. 129 |
| Conjunctive rule | p. 131 |
| Evidential logic rule | p. 131 |
| Causal relational rule | p. 132 |
| Inference | p. 133 |
| Inference at the body proposition level | p. 134 |
| Inference at the rule body level | p. 135 |
| Inference at the rule level | p. 135 |
| Decision making | p. 137 |
| Summary | p. 138 |
| Bibliography | p. 139 |
| p. 141 |
| Machine Learning | p. 143 |
| History of machine learning | p. 143 |
| Human learning | p. 145 |
| Machine learning | p. 147 |
| Categories of machine learning | p. 148 |
| Supervised learning | p. 149 |
| Learning to recognise handwritten characters | p. 151 |
| Examples of supervised learning algorithms | p. 151 |
| A taxonomy of supervised learning algorithms | p. 156 |
| Reinforcement learning | p. 159 |
| Popular reinforcement learning algorithms | p. 160 |
| Unsupervised learning | p. 160 |
| Clustering and discovery algorithms | p. 161 |
| Components of inductive learning algorithms | p. 162 |
| Learning through inductive generalisation | p. 162 |
| Generalisation as search | p. 164 |
| Performance measures | p. 166 |
| Knowledge representation | p. 168 |
| Inductive bias | p. 168 |
| Computational learning theory | p. 169 |
| Goals and accomplishments of machine learning | p. 169 |
| Summary | p. 170 |
| Bibliography | p. 170 |
| p. 177 |
| Cartesian Granule Features | p. 179 |
| Cartesian granule features | p. 179 |
| Why Cartesian granule features? | p. 182 |
| Other usages of Cartesian granules | p. 186 |
| Choice of combination operator | p. 186 |
| Generating Cartesian granule fuzzy sets via fuzzy approaches | p. 187 |
| Generating Cartesian granule fuzzy sets via probability theory | p. 190 |
| Cartesian granule feature rules | p. 193 |
| Approximate reasoning using Cartesian granule feature models | p. 194 |
| Cartesian granule features and fuzzy logic | p. 195 |
| Summary | p. 196 |
| Biblography | p. 196 |
| Learning Cartesian Granule Feature Models | p. 199 |
| Learning using the G_DACG algorithm | p. 199 |
| G_DACG Algorithm | p. 202 |
| Learning Cartesian granule feature fuzzy sets from data | p. 203 |
| Cartesian granule fuzzy set induction example | p. 203 |
| G_DACG algorithm from a prediction perspective | p. 204 |
| Feature Discovery | p. 205 |
| Feature selection and discovery | p. 206 |
| Feature discovery in the G_DACG algorithm | p. 208 |
| Chromosome structure | p. 210 |
| Fitness | p. 210 |
| Modified crossover and mutation | p. 213 |
| Reproduction | p. 213 |
| Feature discovery algorithm in G_DACG | p. 214 |
| Generating linguistic partitions | p. 216 |
| Parameter identification in G_DACG | p. 217 |
| Parameter optimisation in G_DACG | p. 218 |
| Feature weights identification using Powell's algorithm | p. 218 |
| Filter identification using Powell's algorithm | p. 219 |
| A mass assignment-based neuro-fuzzy network | p. 222 |
| A detailed example run of G_DACG | p. 226 |
| Ellipse classification problem | p. 226 |
| Using G_DACG to learn ellipse classifiers | p. 226 |
| Discussion | p. 232 |
| Summary | p. 234 |
| Bibliography | p. 235 |
| p. 239 |
| Analysis of Cartesian Granule Feature Models | p. 241 |
| Experiment variables and analysis | p. 241 |
| Ellipse classification problem | p. 243 |
| An example of ACGF modelling for the ellipse problem | p. 243 |
| Ellipse classification using 2D Cartesian granule features | p. 245 |
| Data centred Cartesian granule features | p. 256 |
| A G_DACG run on the ellipse problem | p. 260 |
| Ellipse results comparison | p. 261 |
| Ellipse problem discussion and summary | p. 263 |
| Sin(X * Y) prediction problem | p. 265 |
| ACGF modelling of the Sin(X * Y) problem | p. 266 |
| A Comparison with other inductive learning techniques | p. 269 |
| Sin(X * Y) problem discussion and summary | p. 271 |
| Why decomposed Cartesian granule feature models? | p. 272 |
| L classification problem | p. 273 |
| Overall discussion | p. 277 |
| Summary and conclusions | p. 278 |
| Bibliography | p. 279 |
| Applications | p. 281 |
| Region classification in image understanding | p. 281 |
| Motivations | p. 282 |
| Knowledge discovery in image understanding | p. 283 |
| Vision problem description | p. 284 |
| Vision dataset | p. 285 |
| Description of region features | p. 286 |
| Region datasets | p. 289 |
| ACGF modelling of the vision problem | p. 292 |
| Vision problem results comparison | p. 295 |
| Vision problem conclusions | p. 295 |
| Modelling Pima diabetes detection problem | p. 296 |
| ACGF modelling of Pima diabetes problem | p. 296 |
| Pima diabetes problem results comparison | p. 299 |
| Modelling the Box-Jenkins gas furnace problem | p. 301 |
| ACGF modelling of the gas furnace problem | p. 301 |
| Gas furnace results comparison | p. 303 |
| Modelling the human operation of a chemical plant controller | p. 303 |
| ACGF modelling of the chemical plant problem | p. 304 |
| Chemical Plant Results Comparison | p. 305 |
| Discussion | p. 305 |
| General conclusions | p. 308 |
| Current and future work directions | p. 308 |
| Summary | p. 310 |
| Bibliography | p. 310 |
| Evolutionary Computation | p. 315 |
| Glossary of Main Symbols | p. 319 |
| Subject Index | p. 321 |
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