Uncertainty and Vagueness in Knowledge Based Systems

This monograph provides a formal framework for the representation and management of uncertainty and vagueness in artificial intelligence. Mathematical modeling is emphasized. The book is self-contained and suitable as an advanced textbook.

Contenu

1. General Considerations of Uncertainty and Vagueness.- 1.1 Artificial Intelligence.- 1.2 Modeling Ignorance.- 1.3 The Scope of the Book.- 2. Introduction.- 2.1 Basic Notations.- 2.2 A Simple Example.- 2.3 Vagueness and Uncertainty.- 3. Vague Data.- 3.1 Basic Concepts.- 3.2 On the Origin of Vague Data.- 3.3 Uncertainty Handling by Means of Layered Contexts.- 3.4 The General Case.- 3.5 Concluding Remarks.- 4. Probability Theory.- 4.1 Basic Concepts.- 4.2 Probabilities on Different Sample Spaces.- 4.3 Bayesian Inference.- 4.4 Classes of Probabilities.- 4.5 Decision Making Aspects.- 4.6 Aggregating Probability Distributions.- 4.7 Concluding Remarks.- 5. Random Sets.- 5.1 Random Variables.- 5.2 The Notion of a Random Set.- 5.3 Decision Making in the Context of Vague Data.- 5.4 The Notion of an Information Source.- 5.5 Concluding Remarks.- 6. Mass Distributions.- 6.1 Basic Concepts.- 6.2 Different Frames of Discernment.- 6.3 Measures for Possibility/Necessity.- 6.4 Generalized Mass Distributions.- 6.5 Decision Making with Mass Distributions.- 6.6 Knowledge Representation with Mass Distributions.- 6.7 Simplifying Assumptions.- 6.8 Concluding Remarks.- 7. On Graphical Representations.- 7.1 Graphs and Trees.- 7.2 Hypergraphs and Hypertrees.- 7.3 Analysis of Simple Hypertrees.- 7.4 Dependency Networks.- 7.5 Triangulated Graphs.- 7.6 Directed Acyclic Graphs.- 7.7 Concluding Remarks.- 8. Modeling Aspects.- 8.1 Rule Based Approaches.- 8.2 Model Based Representations.- 8.3 Dependency Network Based Systems.- 9. Heuristic Models.- 9.1 MYCIN The Certainty Factor Approach.- 9.2 RUM Triangular Norms and Conorms.- 9.3 INFERNO A Bounds Propagation Architecture.- 9.4 Other Heuristic Models.- 10. Fuzzy Set Based Models.- 10.1 Fuzzy Sets.- 10.2 Possibility Distributions.- 10.3Approximate Reasoning.- 10.4 Reasoning with Fuzzy Truth Value.- 10.5 Conclusions.- 11. Reasoning with L-Sets.- 11.1 Knowledge Representation with L-Sets.- 11.2 On the Interpretation of Vague Rules.- 11.3 L-Sets on Product Spaces.- 11.4 Local Computation of Marginal -Sets.- 11.5 The Propagation Algorithm.- 11.6 Aspects of Implementation.- 12. Probability Based Models.- 12.1 The Interpretation of Rules.- 12.2 The Straightforward Use of Probabilities.- 12.3 PROSPECTOR Inference Networks.- 12.4 Decomposable Graphical Models.- 12.5 Propagation Based on Dependency Networks.- 12.6 Concluding Remarks.- 13. Models Based on the Dempster-Shafer Theory of Evidence.- 13.1 The Mathematical Theory of Evidence.- 13.2 Knowledge Representation Aspects.- 13.3 The Straightforward Use of Belief Functions.- 13.4 Belief Functions in Hierarchical Hypothesis Spaces.- 13.5 MacEvidence Belief Propagation in Markov Trees.- 13.6 Conclusions.- 14. Reasoning with Mass Distributions.- 14.1 Matrix Notation for Specializations.- 14.2 Specializations in Product Spaces.- 14.3 Knowledge Representation with Mass Distributions.- 14.4 Local Computations with Mass Distributions.- 14.5 The Propagation Algorithm.- 14.6 Aspects of Implementation.- 15. Related Research.- 15.1 Nonstandard Logics.- 15.2 Integrating Uncertainty Calculi and Logics.- 15.3 Symbolic Methods.- 15.4 Conclusions.- References.