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Measuring Uncertainty within the Theory of Evidence

  • Book
  • © 2018

Overview

Authors:
  1. Simona Salicone

    1. Dipartimento di Elettronica, Informazione e Bioingegneria (DEIB), Politecnico di Milano, Milano, Italy

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    You can also search for this author in PubMed   Google Scholar

  2. Marco Prioli

    1. CERN, Geneva, Switzerland

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    You can also search for this author in PubMed   Google Scholar

  • Defines a rigorous mathematical setting that fosters the identification of an effective uncertainty propagation method
  • Offers a beneficial alternative approach using examples of uncertainty propagation
  • Includes an author-designed, downloadable program that allows readers to interact with the proposed approach

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Table of contents (25 chapters)

  1. Front Matter

    Pages i-xv
    Download chapter PDF

  2. Introduction

    • Simona Salicone, Marco Prioli
    Pages 1-6

  3. The Background of Measurement Uncertainty

    1. Front Matter

      Pages 7-7
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    2. Measurements

      • Simona Salicone, Marco Prioli
      Pages 9-15

    3. Mathematical Methods to Handle Measurement Uncertainty

      • Simona Salicone, Marco Prioli
      Pages 17-36

    4. A First, Preliminary Example

      • Simona Salicone, Marco Prioli
      Pages 37-84

  4. The Mathematical Theory of Evidence

    1. Front Matter

      Pages 85-85
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    2. Introduction: Probability and Belief Functions

      • Simona Salicone, Marco Prioli
      Pages 87-92

    3. Basic Definitions of the Theory of Evidence

      • Simona Salicone, Marco Prioli
      Pages 93-105

    4. Particular Cases of the Theory of Evidence

      • Simona Salicone, Marco Prioli
      Pages 107-128

    5. Operators Between Possibility Distributions

      • Simona Salicone, Marco Prioli
      Pages 129-152

    6. The Joint Possibility Distributions

      • Simona Salicone, Marco Prioli
      Pages 153-160

    7. The Combination of the Possibility Distributions

      • Simona Salicone, Marco Prioli
      Pages 161-162

    8. The Comparison of the Possibility Distributions

      • Simona Salicone, Marco Prioli
      Pages 163-165

    9. The Probability-Possibility Transformations

      • Simona Salicone, Marco Prioli
      Pages 167-182

  5. The Fuzzy Set Theory and the Theory of Evidence

    1. Front Matter

      Pages 183-183
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    2. A Short Review of the Fuzzy Set Theory

      • Simona Salicone, Marco Prioli
      Pages 185-193

    3. The Relationship Between the Fuzzy Set Theory and the Theory of Evidence

      • Simona Salicone, Marco Prioli
      Pages 195-203

  6. Measurement Uncertainty Within the Mathematical Framework of the Theory of Evidence

    1. Front Matter

      Pages 205-205
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    2. Introduction: Toward an Alternative Representation of the Measurement Results

      • Simona Salicone, Marco Prioli
      Pages 207-208
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Keywords

About this book

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 tointeract 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. 



Authors and Affiliations

  • Dipartimento di Elettronica, Informazione e Bioingegneria (DEIB), Politecnico di Milano, Milano, Italy

    Simona Salicone

  • CERN, Geneva, Switzerland

    Marco Prioli

About the authors

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). 

Bibliographic Information

  • Book Title: Measuring Uncertainty within the Theory of Evidence

  • Authors: Simona Salicone, Marco Prioli

  • Series Title: Springer Series in Measurement Science and Technology

  • DOI: https://doi.org/10.1007/978-3-319-74139-0

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG, part of Springer Nature 2018

  • Hardcover ISBN: 978-3-319-74137-6Published: 07 May 2018

  • Softcover ISBN: 978-3-030-08924-5Published: 24 January 2019

  • eBook ISBN: 978-3-319-74139-0Published: 23 April 2018

  • Series ISSN: 2198-7807

  • Series E-ISSN: 2198-7815

  • Edition Number: 1

  • Number of Pages: XV, 330

  • Number of Illustrations: 13 b/w illustrations, 141 illustrations in colour

  • Topics: Probability Theory and Stochastic Processes

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