Measuring Uncertainty within the Theory of Evidence
Published on 24. January 2019
Book
Paperback/Softback
XV, 330 pages
978-3-030-08924-5 (ISBN)
Description
This monograph considers the evaluation and expression of measurement uncertainty within the mathematical framework of the Theory of Evidence. With a new perspective on the metrology science, the text paves the way for innovative applications in a wide range of areas. Building on Simona Salicone's Measurement Uncertainty: An Approach via the Mathematical Theory of Evidence, the material covers further developments of the Random Fuzzy Variable (RFV) approach to uncertainty and provides a more robust mathematical and metrological background to the combination of measurement results that leads to a more effective RFV combination method.
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 to interact 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.
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 to interact 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.
More details
Product info
Previously published in hardcover
Series
Edition
Softcover reprint of the original 1st ed. 2018
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
141 farbige Abbildungen, 13 s/w Abbildungen
141 Illustrations, color; 13 Illustrations, black and white; XV, 330 p. 154 illus., 141 illus. in color.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 19 mm
Weight
528 gr
ISBN-13
978-3-030-08924-5 (9783030089245)
DOI
10.1007/978-3-319-74139-0
Schweitzer Classification
Other editions
Additional editions
Simona Salicone | Marco Prioli
Measuring Uncertainty within the Theory of Evidence
Advances within the Theory of Evidence
Book
05/2018
Springer
€128.39
Shipment within 10-15 days
Persons
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).
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).
Content
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.