Measuring Uncertainty within the Theory of Evidence [electronic resource] /
Salicone, Simona.author.
Prioli, Marco.author.
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. .
Includes bibliographical references and index.
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.
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. .
Probabilities.
Probability Theory and Stochastic Processes.