Preface |
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V | |
Notations |
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VII | |
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1 "Classical" Expert Systems |
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1 | |
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1 | |
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3 | |
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1.3 Structure of Rule-Based Expert Systems |
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4 | |
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1.4 Reasoning in an Expert System |
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5 | |
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9 | |
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10 | |
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2 Knowledge Representation |
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13 | |
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2.1 Data, Information and Knowledge |
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13 | |
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14 | |
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19 | |
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2.4 Inference Rules in Classical Logic |
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22 | |
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23 | |
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24 | |
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27 | |
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3 Uncertainty and Classical Theory of Probability |
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31 | |
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3.1 Taxonomy of Imperfection |
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31 | |
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3.2 Usual and Precise Meaning |
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33 | |
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3.3 Experiments and Events |
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35 | |
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3.4 Formal Definition of Events |
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39 | |
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3.5 Defining Probabilities |
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41 | |
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3.6 Defining Probabilities (II) |
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44 | |
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47 | |
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49 | |
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3.9 Random Variables and Distributions |
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50 | |
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3.10 Expectation and Variance |
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51 | |
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3.11 Examples of Discrete Distributions |
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56 | |
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3.12 Continuous Distributions |
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60 | |
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3.13 Examples of Continuous Distributions. Normal |
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64 | |
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3.14 Examples of Continuous Distributions. Chi-square |
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67 | |
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3.15 Student and Fisher-Snedecor Distributions |
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70 | |
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3.16 Formal definition of Random Variables |
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73 | |
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3.17 Probabilities of Formulas |
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76 | |
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82 | |
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89 | |
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4.1 Inferring Scientific Truth: Tests of Significance |
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89 | |
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4.2 Relation "Alternative Hypothesis - Null Hypothesis" |
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91 | |
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4.3 Hypothesis Testing, the Classical Approach |
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93 | |
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4.4 Examples: Comparing Means |
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94 | |
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4.5 Comparing Means, the Practical Approach |
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104 | |
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4.6 Paired and Unpaired Tests |
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105 | |
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4.7 Example: Comparing Proportions |
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107 | |
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4.8 Goodness-of-Fit: Chi-square |
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112 | |
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4.9 Other Goodness-of-Fit Tests |
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119 | |
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4.10 Nonparametric Tests. Wilcoxon/Mann-Whitney |
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120 | |
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4.11 Analysis of Variance |
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124 | |
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126 | |
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127 | |
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5 Bayesian (Belief) Networks |
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133 | |
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5.1 Uncertain Production Rules |
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133 | |
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5.2 Bayesian (Belief, Causal) Networks |
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135 | |
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5.3 Examples of Bayesian Networks |
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138 | |
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144 | |
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5.5 Bias of the Bayesian (Probabilistic) Method |
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148 | |
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148 | |
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6 Certainty Factors Theory |
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153 | |
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153 | |
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154 | |
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6.3 Certainty Factors and Measures of Belief and Disbelief |
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156 | |
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158 | |
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161 | |
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161 | |
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163 | |
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7.3 Dempster-Shafer Theory |
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165 | |
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7.4 The Pignistic Transform |
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171 | |
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7.5 Combining Beliefs. The Dempster's Formula |
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172 | |
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7.6 Difficulties with Dempster-Shafer's Theory |
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176 | |
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7.7 Specializations and the Transferable Belief Model |
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177 | |
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7.8 Conditional Beliefs and the Generalized Bayesian Theorem |
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180 | |
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181 | |
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187 | |
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8.1 Necessity and Possibility Measures |
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187 | |
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8.2 Conditional Possibilities |
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190 | |
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193 | |
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195 | |
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9.1 Fuzzy Sets, Fuzzy Numbers, Fuzzy Relations |
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195 | |
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9.2 Fuzzy Propositions and Fuzzy Logic |
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204 | |
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206 | |
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212 | |
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9.5 Approximate Reasoning |
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218 | |
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224 | |
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9.7 Approach by Precision Degrees |
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226 | |
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228 | |
10 Review |
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233 | |
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10.1 Review of Uncertainty and Imprecision |
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233 | |
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239 | |
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10.3 Perception-Based Theory |
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242 | |
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244 | |
References |
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247 | |
Index |
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251 | |