Possibility theory: an approach to computerized processing of uncertainty
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English French |
| Published: |
New York [u.a.]
Plenum Press
1988
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 263 S. graph. Darst. |
| ISBN: | 0306425203 |
Staff View
MARC
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| 240 | 1 | 0 | |a Théorie des possibilités |
| 245 | 1 | 0 | |a Possibility theory |b an approach to computerized processing of uncertainty |c Didier Dubois and Henri Prade |
| 264 | 1 | |a New York [u.a.] |b Plenum Press |c 1988 | |
| 300 | |a XVI, 263 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Ensembles flous - Informatique | |
| 650 | 7 | |a Informatique |2 ram | |
| 650 | 4 | |a Possibilité - Informatique | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Fuzzy sets |x Data processing | |
| 650 | 4 | |a Possibility |x Data processing | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
1. Measures of Possibility and Fuzzy Sets 1
1.1. Imprecision and Uncertainty 1
1.2. Traditional Models of Imprecision and Uncertainty .... 4
1.3. Confidence Measures 7
1.3.1. Measures of Possibility and of Necessity 8
1.3.2. Possibility and Probability 10
1.4. Fuzzy Sets 13
1.5. Elementary Fuzzy Set Operations 17
1.6. Practical Methods for Determining Membership Functions . 19
1.6.1. Vague Categories as Perceived by an Individual . . 19
1.6.2. Fuzzy Sets Constructed from Statistical Data .... 20
1.6.3. Remarks on the Set of Degrees of Membership . . 24
1.7. Confidence Measures for a Fuzzy Event 25
1.8. Fuzzy Relations and Cartesian Products of Fuzzy Sets ... 27
References 30
2. The Calculus of Fuzzy Quantities 33
2.1. Definitions and a Fundamental Principle 33
2.1.1. Fuzzy Quantities, Fuzzy Intervals, Fuzzy Numbers . 33
2.1.2. The Extension Principle 36
2.2. Calculus of Fuzzy Quantities with Noninteractive Variables 38
2.2.1. Fundamental Result 39
2.2.2. Relation to Interval Analysis 42
2.2.3. Application to Standard Operations 43
xiii
xiv Contents
2.2.4. The Problem of Equivalent Representations of a
Function 47
2.3. Practical Calculation with Fuzzy Intervals 48
2.3.1. Parametric Representation of a Fuzzy Interval ... 48
2.3.2. Exact Practical Calculation with the Four Arithmetic
Operations 50
2.3.3. Approximate Calculation of Functions of Fuzzy
Intervals 52
2.4. Further Calculi of Fuzzy Quantities 53
2.4.1. Pessimistic Calculus of Fuzzy Quantities with
Interactive Variables 54
2.4.2. Optimistic Calculus of Fuzzy Quantities with
Noninteractive Variables 56
2.5. Illustrative Examples 57
2.5.1. Estimation of Resources in a Budget 57
2.5.2. Calculation of a PERT Analysis with Fuzzy Duration
Estimates 60
2.5.3. A Problem in the Control of a Machine Tool ... 63
Appendix: Computer Programs 66
References 71
3. The Use of Fuzzy Sets for the Evaluation and Ranking of
Objects 73
3.1. A Quantitative Approach to Multiaspect Choice 73
3.1.1. Basic Principles of the Approach 74
3.1.2. Fuzzy Set Theoretic Operations 77
3.1.3. Application to the Combination of Criteria .... 86
3.1.4. Identification of Operators 94
3.1.5. Example 95
3.2. Comparison of Imprecise Evaluations 98
3.2.1. Comparison of a Real Number and a Fuzzy Interval 99
3.2.2. Comparison of Two Fuzzy Intervals 101
3.2.3. Ordering of n Fuzzy Intervals 105
3.2.4. Computer Implementation 106
3.2.5. Example 107
Appendix: Computer Programs 108
References 113
4. Models for Approximate Reasoning in Expert Systems .... 117
4.1. Remarks on Modeling Imprecision and Uncertainty .... 117
4.1.1. Credibility and Plausibility 118
4.1.2. Decomposable Measures 121
Contents xv
4.1.3. Vague Propositions 123
4.1.4. Evaluating the Truth Value of a Proposition .... 123
4.2. Reasoning from Uncertain Premises 127
4.2.1. Deductive Inference with Uncertain Premises . . . 130
4.2.2. Complex Premises 136
4.2.3. Combining Degrees of Uncertainty Relative to the
Same Proposition 136
4.3. Inference from Vague or Fuzzy Premises 142
4.3.1. Representation of the Rule if X is A, then Y is 5 142
4.3.2. Generalized Modus Ponens 143
4.3.3. Complex Premises 146
4.3.4. Combining Possibility Distributions 146
4.4. Brief Summary of Current Work and Systems 147
4.5. Example 148
Appendix A 152
Appendix B: Computer Programs 158
References 175
5. Heuristic Search in an Imprecise Environment, and Fuzzy
Programming 181
5.1. Heuristic Search in an Imprecise Environment 182
5.1.1. A and A* Algorithms 182
5.1.2. The Classical Traveling Salesman Problem
(Reminder) 183
5.1.3. Heuristic Search with Imprecise Evaluations .... 185
5.1.4. Heuristic Search with Fuzzy Values 189
5.2. An Example of Fuzzy Programming: Tracing the Execution
of an Itinerary Specified in Imprecise Terms 191
5.2.1. Execution and Chaining of Instructions 193
5.2.2. Illustrative Example 195
5.2.3. Problems Arising in Fuzzy Programming 202
5.2.4. Concluding Remarks 207
Appendix: Computer Programs 208
A.I. Selection of the Smallest of N Fuzzy Numbers . . 208
A.2. Tracing Imprecisely Specified Itineraries 209
References 214
6. Handling of Incomplete or Uncertain Data and Vague Queries
in Database Applications 217
6.1. Representation of Incomplete or Uncertain Data 218
6.1.1. Representing Data by Means of Possibility
Distributions 218
xvi Contents
6.1.2. Differences and Similarities with Other Fuzzy
Approaches 221
6.1.3. Dependencies and Possibilistic Information .... 224
6.2. The Extended Relational Algebra and the Corresponding
Query Language 225
6.2.1. Generalization of e Selection 225
6.2.2. Cartesian Product, © Join, and Projection 232
6.2.3. Union and Intersection—Redundancy 235
6.2.4. Queries Employing Other Operations 236
6.3. Example 237
6.3.1. Representation of Data 237
6.3.2. Examples of Queries 240
6.4. Conclusion 243
Appendix: Computer Program 244
A.I. Data Structures 244
A.2. Representation of Queries 246
A.3. Description of Implemeted Procedures 247
References 257
Index 261
|
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| institution | BVB |
| isbn | 0306425203 |
| language | English French |
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| spelling | Dubois, Didier 1952- Verfasser (DE-588)172049415 aut Théorie des possibilités Possibility theory an approach to computerized processing of uncertainty Didier Dubois and Henri Prade New York [u.a.] Plenum Press 1988 XVI, 263 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ensembles flous - Informatique Informatique ram Possibilité - Informatique Datenverarbeitung Fuzzy sets Data processing Possibility Data processing Fuzzy-Logik (DE-588)4341284-1 gnd rswk-swf Entscheidungstheorie (DE-588)4138606-1 gnd rswk-swf Fuzzy-Menge (DE-588)4061868-7 gnd rswk-swf Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Fuzzy-Menge (DE-588)4061868-7 s Datenverarbeitung (DE-588)4011152-0 s DE-604 Fuzzy-Logik (DE-588)4341284-1 s Entscheidungstheorie (DE-588)4138606-1 s Prade, Henri 1953- Verfasser (DE-588)170518280 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001402312&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dubois, Didier 1952- Prade, Henri 1953- Possibility theory an approach to computerized processing of uncertainty Ensembles flous - Informatique Informatique ram Possibilité - Informatique Datenverarbeitung Fuzzy sets Data processing Possibility Data processing Fuzzy-Logik (DE-588)4341284-1 gnd Entscheidungstheorie (DE-588)4138606-1 gnd Fuzzy-Menge (DE-588)4061868-7 gnd Datenverarbeitung (DE-588)4011152-0 gnd |
| subject_GND | (DE-588)4341284-1 (DE-588)4138606-1 (DE-588)4061868-7 (DE-588)4011152-0 |
| title | Possibility theory an approach to computerized processing of uncertainty |
| title_alt | Théorie des possibilités |
| title_auth | Possibility theory an approach to computerized processing of uncertainty |
| title_exact_search | Possibility theory an approach to computerized processing of uncertainty |
| title_full | Possibility theory an approach to computerized processing of uncertainty Didier Dubois and Henri Prade |
| title_fullStr | Possibility theory an approach to computerized processing of uncertainty Didier Dubois and Henri Prade |
| title_full_unstemmed | Possibility theory an approach to computerized processing of uncertainty Didier Dubois and Henri Prade |
| title_short | Possibility theory |
| title_sort | possibility theory an approach to computerized processing of uncertainty |
| title_sub | an approach to computerized processing of uncertainty |
| topic | Ensembles flous - Informatique Informatique ram Possibilité - Informatique Datenverarbeitung Fuzzy sets Data processing Possibility Data processing Fuzzy-Logik (DE-588)4341284-1 gnd Entscheidungstheorie (DE-588)4138606-1 gnd Fuzzy-Menge (DE-588)4061868-7 gnd Datenverarbeitung (DE-588)4011152-0 gnd |
| topic_facet | Ensembles flous - Informatique Informatique Possibilité - Informatique Datenverarbeitung Fuzzy sets Data processing Possibility Data processing Fuzzy-Logik Entscheidungstheorie Fuzzy-Menge |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001402312&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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