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E-raamat: Management of Knowledge Imperfection in Building Intelligent Systems

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There are many good AI books. Usually they consecrate at most one or two chapters to the imprecision knowledge processing. To our knowledge this is among the few books to be entirely dedicated to the treatment of knowledge imperfection when bui- ing intelligent systems. We consider that an entire book should be focused on this important aspect of knowledge processing. The expected audience for this book - cludes undergraduate students in computer science, IT&C, mathematics, business, medicine, etc. , graduates, specialists and researchers in these fields. The subjects treated in the book include expert systems, knowledge representation, reasoning under knowledge Imperfection (Probability Theory, Possibility Theory, Belief Theory, and Approximate Reasoning). Most of the examples discussed in details throughout the book are from the medical domain. Each chapter ends with a set of carefully pe- gogically chosen exercises, which complete solution provided. Their understanding will trigger the comprehension of the theoretical notions, concepts and results. Chapter 1 is dedicated to the review of expert systems. Hence are briefly discussed production rules, structure of ES, reasoning in an ES, and conflict resolution. Chapter 2 treats knowledge representation. That includes the study of the differences between data, information and knowledge, logical systems with focus on predicate calculus, inference rules in classical logic, semantic nets and frames.
Preface V
Notations VII
1 "Classical" Expert Systems
1
1.1 Production Rules
1
1.2 Expert Systems
3
1.3 Structure of Rule-Based Expert Systems
4
1.4 Reasoning in an Expert System
5
1.5 Conflicts Resolution
9
1.6 Solved Exercises
10
2 Knowledge Representation
13
2.1 Data, Information and Knowledge
13
2.2 Logical Systems
14
2.3 Predicate Calculus
19
2.4 Inference Rules in Classical Logic
22
2.5 Semantic Nets
23
2.6 Frames
24
2.7 Solved Exercises
27
3 Uncertainty and Classical Theory of Probability
31
3.1 Taxonomy of Imperfection
31
3.2 Usual and Precise Meaning
33
3.3 Experiments and Events
35
3.4 Formal Definition of Events
39
3.5 Defining Probabilities
41
3.6 Defining Probabilities (II)
44
3.7 Bayes' Theorem
47
3.8 Misleading Aspects
49
3.9 Random Variables and Distributions
50
3.10 Expectation and Variance
51
3.11 Examples of Discrete Distributions
56
3.12 Continuous Distributions
60
3.13 Examples of Continuous Distributions. Normal
64
3.14 Examples of Continuous Distributions. Chi-square
67
3.15 Student and Fisher-Snedecor Distributions
70
3.16 Formal definition of Random Variables
73
3.17 Probabilities of Formulas
76
3.18 Solved Exercises
82
4 Statistical Inference
89
4.1 Inferring Scientific Truth: Tests of Significance
89
4.2 Relation "Alternative Hypothesis - Null Hypothesis"
91
4.3 Hypothesis Testing, the Classical Approach
93
4.4 Examples: Comparing Means
94
4.5 Comparing Means, the Practical Approach
104
4.6 Paired and Unpaired Tests
105
4.7 Example: Comparing Proportions
107
4.8 Goodness-of-Fit: Chi-square
112
4.9 Other Goodness-of-Fit Tests
119
4.10 Nonparametric Tests. Wilcoxon/Mann-Whitney
120
4.11 Analysis of Variance
124
4.12 Summary
126
4.13 Solved Exercises
127
5 Bayesian (Belief) Networks
133
5.1 Uncertain Production Rules
133
5.2 Bayesian (Belief, Causal) Networks
135
5.3 Examples of Bayesian Networks
138
5.4 Software
144
5.5 Bias of the Bayesian (Probabilistic) Method
148
5.6 Solved Exercises
148
6 Certainty Factors Theory
153
6.1 Certainty Factors
153
6.2 Stanford Algebra
154
6.3 Certainty Factors and Measures of Belief and Disbelief
156
6.4 Solved Exercises
158
7 Belief Theory
161
7.1 Belief Approach
161
7.2 Agreement Measures
163
7.3 Dempster-Shafer Theory
165
7.4 The Pignistic Transform
171
7.5 Combining Beliefs. The Dempster's Formula
172
7.6 Difficulties with Dempster-Shafer's Theory
176
7.7 Specializations and the Transferable Belief Model
177
7.8 Conditional Beliefs and the Generalized Bayesian Theorem
180
7.9 Solved Exercises
181
8 Possibility Theory
187
8.1 Necessity and Possibility Measures
187
8.2 Conditional Possibilities
190
8.3 Exercises
193
9 Approximate Reasoning
195
9.1 Fuzzy Sets, Fuzzy Numbers, Fuzzy Relations
195
9.2 Fuzzy Propositions and Fuzzy Logic
204
9.3 Hedges
206
9.4 Fuzzy Logic
212
9.5 Approximate Reasoning
218
9.6 Defuzzification
224
9.7 Approach by Precision Degrees
226
9.8 Solved Exercises
228
10 Review 233
10.1 Review of Uncertainty and Imprecision
233
10.2 Production Rules
239
10.3 Perception-Based Theory
242
10.4 Solved Exercises
244
References 247
Index 251