Measuring Uncertainty within the Theory of Evidence
Springer International Publishing (Verlag)
978-3-030-08924-5 (ISBN)
While the first part of the book introduces measurement uncertainty, the Theory of Evidence, and fuzzy sets, the following parts bring together these concepts and derive an effective methodology for the evaluation and expression of measurement uncertainty. A supplementary downloadable program allows the readers tointeract with the proposed approach by generating and combining RFVs through custom measurement functions. With numerous examples of applications, this book provides a comprehensive treatment of the RFV approach to uncertainty that is suitable for any graduate student or researcher with interests in the measurement field.
Simona Salicone is Associate Professor of electrical and electronic measurements in the Dipartimento di Elettronica, Informazione e Bioingegneria (DEIB), Politecnico di Milano. Her principal research interests are the analysis of advanced mathematical methods for uncertainty representation and estimation, and she has contributed to the development and application of the mathematical Theory of Evidence to the expression and evaluation of uncertainty in measurement. Marco Prioli is an IEEE Instrumentation and Measurement Society member. He is also a memeber of the Italian Association for Electrical and Electronic Measurements (GMEE).
1. Introduction.- Part I: The background of the Measurement Uncertainty.- 2. Measurements.- 3. Mathematical Methods to handle Measurement Uncertainty.- 4. A first, preliminary example.- Part II: The mathematical Theory of the Evidence.- 5. Introduction: probability and belief functions.- 6. Basic definitions of the Theory of Evidence.- 7. Particular cases of the Theory of Evidence.- 8. Operators between possibility distributions.- 9. The joint possibility distributions.- 10. The combination of the possibility distributions.- 11. The comparison of the possibility distributions.- 12. The Probability-Possibility Transformations.- Part III: The Fuzzy Set Theory and the Theory of the Evidence.- 13. A short review of the Fuzzy Set Theory.- 14. The relationship between the Fuzzy Set Theory and the Theory of Evidence.- Part IV: Measurement Uncertainty within the mathematical framework of the Theory of the Evidence.- 15. Introduction: towards an alternative representation of the Measurement Results.- 16. Random-Fuzzy Variables and Measurement Results.- 17. The Joint Random-Fuzzy variables.- 18. The Combination of the Random-Fuzzy Variables.- 19. The Comparison of the Random-Fuzzy Variables.- 20. Measurement Uncertainty within Fuzzy Inference Systems.- Part V: Application examples.- 21. Phantom Power measurement.- 22. Characterization of a resistive voltage divider.- 23. Temperature measurement update.- 24. The Inverted Pendulum.- 25. Conclusion.- References.- Index.
| Erscheinungsdatum | 04.02.2019 |
|---|---|
| Reihe/Serie | Springer Series in Measurement Science and Technology |
| Zusatzinfo | XV, 330 p. 154 illus., 141 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 534 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik |
| Schlagworte | Evidence-Based Probability • Fuzzy set theory • Inverted Pendulum • Joint Possibility distributions • Measurement Uncertainty • phantom power measurement • Probability-Possibility transformations • Probability Theory • random fuzzy variables • theory of evidence |
| ISBN-10 | 3-030-08924-X / 303008924X |
| ISBN-13 | 978-3-030-08924-5 / 9783030089245 |
| Zustand | Neuware |
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