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Measuring Uncertainty within the Theory of Evidence

  • Simona Salicone
  • Marco Prioli

Table of contents

  1. Front Matter
    Pages i-xv
  2. Simona Salicone, Marco Prioli
    Pages 1-6
  3. The Background of Measurement Uncertainty

    1. Front Matter
      Pages 7-7
    2. Simona Salicone, Marco Prioli
      Pages 9-15
    3. Simona Salicone, Marco Prioli
      Pages 17-36
    4. Simona Salicone, Marco Prioli
      Pages 37-84
  4. The Mathematical Theory of Evidence

    1. Front Matter
      Pages 85-85
    2. Simona Salicone, Marco Prioli
      Pages 87-92
    3. Simona Salicone, Marco Prioli
      Pages 93-105
    4. Simona Salicone, Marco Prioli
      Pages 107-128
    5. Simona Salicone, Marco Prioli
      Pages 129-152
    6. Simona Salicone, Marco Prioli
      Pages 153-160
    7. Simona Salicone, Marco Prioli
      Pages 161-162
    8. Simona Salicone, Marco Prioli
      Pages 163-165
    9. Simona Salicone, Marco Prioli
      Pages 167-182
  5. The Fuzzy Set Theory and the Theory of Evidence

    1. Front Matter
      Pages 183-183
    2. Simona Salicone, Marco Prioli
      Pages 185-193
  6. Measurement Uncertainty Within the Mathematical Framework of the Theory of Evidence

    1. Front Matter
      Pages 205-205
    2. Simona Salicone, Marco Prioli
      Pages 209-221
    3. Simona Salicone, Marco Prioli
      Pages 223-225
    4. Simona Salicone, Marco Prioli
      Pages 227-267
    5. Simona Salicone, Marco Prioli
      Pages 269-271
    6. Simona Salicone, Marco Prioli
      Pages 273-288
  7. Application Examples

    1. Front Matter
      Pages 289-289
    2. Simona Salicone, Marco Prioli
      Pages 291-302
    3. Simona Salicone, Marco Prioli
      Pages 303-308
    4. Simona Salicone, Marco Prioli
      Pages 309-314
    5. Simona Salicone, Marco Prioli
      Pages 315-321
    6. Simona Salicone, Marco Prioli
      Pages 323-323
  8. Back Matter
    Pages 325-330

About this book

Introduction

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. 

Keywords

Evidence-Based Probability Joint Possibility distributions Measurement Uncertainty Probability Theory Probability-Possibility transformations fuzzy set theory theory of evidence inverted pendulum phantom power measurement random fuzzy variables

Authors and affiliations

  • Simona Salicone
    • 1
  • Marco Prioli
    • 2
  1. 1.Dipartimento di ElettronicaInformazione e Bioingegneria (DEIB), Politecnico di MilanoMilanoItaly
  2. 2.CERNGenevaSwitzerland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-74139-0
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-74137-6
  • Online ISBN 978-3-319-74139-0
  • Series Print ISSN 2198-7807
  • Series Online ISSN 2198-7815
  • Buy this book on publisher's site
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