Measuring Uncertainty within the Theory of Evidence (eBook)

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.