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|a 10.1007/978-1-4684-5287-7
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|a Dubois, Didier.
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|4 http://id.loc.gov/vocabulary/relators/aut
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|a Possibility Theory
|h [electronic resource] :
|b An Approach to Computerized Processing of Uncertainty /
|c by Didier Dubois, Henri Prade.
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|a 1st ed. 1988.
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|a New York, NY :
|b Springer US :
|b Imprint: Springer,
|c 1988.
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|a 280 p.
|b online resource.
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|a 1. Measures of Possibility and Fuzzy Sets -- 1.1. Imprecision and Uncertainty -- 1.2. Traditional Models of Imprecision and Uncertainty -- 1.3. Confidence Measures -- 1.4. Fuzzy Sets -- 1.5. Elementary Fuzzy Set Operations -- 1.6. Practical Methods for Determining Membership Functions -- 1.7. Confidence Measures for a Fuzzy Event -- 1.8. Fuzzy Relations and Cartesian Products of Fuzzy Sets -- References -- 2. The Calculus of Fuzzy Quantities -- 2.1. Definitions and a Fundamental Principle -- 2.2. Calculus of Fuzzy Quantities with Noninteractive Variables -- 2.3. Practical Calculation with Fuzzy Intervals -- 2.4. Further Calculi of Fuzzy Quantities -- 2.5. Illustrative Examples -- Appendix: Computer Programs -- References -- 3. The Use of Fuzzy Sets for the Evaluation and Ranking of Objects -- 3.1. A Quantitative Approach to Multiaspect Choice -- 3.2. Comparison of Imprecise Evaluations -- Appendix: Computer Programs -- References -- 4. Models for Approximate Reasoning in Expert Systems -- 4.1. Remarks on Modeling Imprecision and Uncertainty -- 4.2. Reasoning from Uncertain Premises -- 4.3. Inference from Vague or Fuzzy Premises -- 4.4. Brief Summary of Current Work and Systems -- 4.5. Example -- Appendix A. -- Appendix B: Computer Programs -- References -- 5. Heuristic Search in an Imprecise Environment, and Fuzzy Programming -- 5.1. Heuristic Search in an Imprecise Environment -- 5.2. An Example of Fuzzy Programming: Tracing the Execution of an Itinerary Specified in Imprecise Terms -- Appendix: Computer Programs -- A.1. Selection of “the Smallest” of N Fuzzy Numbers -- A.2. Tracing Imprecisely Specified Itineraries -- References -- 6. Handling of Incomplete or Uncertain Data and Vague Queries in Database Applications -- 6.1. Representation of Incomplete or Uncertain Data -- 6.2. The Extended Relational Algebra and the Corresponding Query Language -- 6.3. Example -- 6.4. Conclusion -- Appendix: Computer Program -- A.1. Data Structures -- A.2. Representation of Queries -- A.3. Description of Implemeted Procedures -- References.
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|a In the evolution of scientific theories, concern with uncertainty is almost invariably a concomitant of maturation. This is certainly true of the evolution· of physics, economics, operations research, communication sciences, and a host of other fields. And it is true of what has been happening more recently in the area of artificial intelligence, most notably in the development of theories relating to the management of uncertainty in knowledge-based systems. In science, it is traditional to deal with uncertainty through the use of probability theory. In recent years, however, it has become increasingly clear that there are some important facets of uncertainty which do not lend themselves to analysis by classical probability-based methods. One such facet is that of lexical elasticity, which relates to the fuzziness of words in natural languages. As a case in point, even a simple relation X, Y, and Z, expressed as if X is small and Y is very large then between Z is not very small, does not lend itself to a simple interpretation within the framework of probability theory by reason of the lexical elasticity of the predicates small and large.
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