Measuring Uncertainty within the Theory of Evidence / by Simona Salicone, Marco Prioli.

Salicone, Simona author., Author,
1st ed. 2018.
Cham : Springer International Publishing : Imprint: Springer, 2018.
Mathematics and Statistics (Springer-11649)
Springer series in measurement science and technology 2198-7807
Springer Series in Measurement Science and Technology, 2198-7807
1 online resource (XV, 330 pages) : 154 illustrations, 141 illustrations in color.
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Probability Theory and Stochastic Processes. (search)
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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. .
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
Prioli, Marco, author., Author,
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Publisher Number:
10.1007/978-3-319-74139-0 doi
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