From intervals to ? : towards a general description of validated uncertainty
 Responsibility
 Vladik Kreinovich, Graçaliz Pereira Dimuro, Antônio Carlos da Rocha Costa.
 Imprint
 Cham : Springer, 2023.
 Physical description
 1 online resource (125 p.).
 Series
 Studies in computational intelligence ; v. 1041.
Online
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Description
Creators/Contributors
 Author/Creator
 Kreinovich, Vladik.
 Contributor
 Dimuro, Graçaliz Pereira.
 Rocha Costa, Antônio Carlos da.
Contents/Summary
 Bibliography
 References  4 A General Description of Measuring Devices: Second StepPairs of Compatible Outcomes  4.1 How Do We Describe Uncertainty: Main Idea  4.2 Comment on Quantum Measurements  4.3 Some Pairs of Outcomes Are Compatible (Close), Some Are Not  4.4 The Existence of a Full Theory Makes the Set of All Compatible Pairs of Outcomes Algorithmically Listable  4.5 Conclusion: Algorithmically Listable Set of Compatible Pairs of Outcomes  4.6 Description in Terms of Existing Mathematical Structures  4.7 Example 1: Interval Uncertainty  4.8 Example 2: Counting
 Contents

 Motivation and Outline. A General Description of Measuring Devices: Plan. A General Description of Measuring Devices: First Step  Finite Set of Possible Outcomes. A General Description of Measuring Devices: Second Step  Pairs of Compatible Outcomes. A General Description of Measuring Devices: Third Step  Subsets of Compatible Outcomes. A General Description of Measuring Devices: Fourth Step  Conditional Statements about Possible Outcomes. A General Description of Measuring Devices: Fifth Step  Disjunctive Conditional Statements about the Possible Outcomes. A General Description of Measuring Devices: Summary. Physical Quantities: A General Description. Properties of Physical Quantities. Future Work.
 (source: Nielsen Book Data)
 Publisher's summary

This book is about methodological aspects of uncertainty propagation in data processing. Uncertainty propagation is an important problem: while computer algorithms efficiently process data related to many aspects of their lives, most of these algorithms implicitly assume that the numbers they process are exact. In reality, these numbers come from measurements, and measurements are never 100% exact. Because of this, it makes no sense to translate 61 kg into pounds and get the resultas computers dowith 13 digit accuracy. In many casese.g., in celestial mechanicsthe state of a system can be described by a few numbers: the values of the corresponding physical quantities. In such cases, for each of these quantities, we know (at least) the upper bound on the measurement error. This bound is either provided by the manufacturer of the measuring instrumentor is estimated by the user who calibrates this instrument. However, in many other cases, the description of the system is more complex than a few numbers: we need a function to describe a physical field (e.g., electromagnetic field); we need a vector in Hilbert space to describe a quantum state; we need a pseudoRiemannian space to describe the physical spacetime, etc. To describe and process uncertainty in all such cases, this book proposes a general methodologya methodology that includes intervals as a particular case. The book is recommended to students and researchers interested in challenging aspects of uncertainty analysis and to practitioners who need to handle uncertainty in such unusual situations.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2023
 Series
 Studies in Computational Intelligence ; v.1041
 Note
 5.3 Information About Compatible Pairs Is Sufficient For Intervals
 ISBN
 9783031205699 (electronic bk.)
 3031205693 (electronic bk.)
 3031205685
 9783031205682
 DOI
 10.1007/9783031205699