From intervals to -? : towards a general description of validated uncertainty / Vladik Kreinovich, Graçaliz Pereira Dimuro, Antônio Carlos da Rocha Costa.
Kreinovich, Vladik.; Dimuro, Graçaliz Pereira.; Rocha Costa, Antônio Carlos da.
2023
Q375
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Title From intervals to -? : towards a general description of validated uncertainty / Vladik Kreinovich, Graçaliz Pereira Dimuro, Antônio Carlos da Rocha Costa.
Author Kreinovich, Vladik.
ISBN 9783031205699 (electronic bk.)
3031205693 (electronic bk.)
3031205685
9783031205682
DOI https://doi.org/10.1007/978-3-031-20569-9
Imprint Cham : Springer, 2023.
Language English
Description 1 online resource (125 p.).
Other Standard Identifiers 10.1007/978-3-031-20569-9 doi
Call Number Q375
Dewey Decimal Classification 003/.54
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 pseudo-Riemannian space to describe the physical space-time, 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.
Note 5.3 Information About Compatible Pairs Is Sufficient For Intervals
Bibliography, etc. Note References -- 4 A General Description of Measuring Devices: Second Step-Pairs 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
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed December 8, 2022).
Added Author Dimuro, Graçaliz Pereira.
Rocha Costa, Antônio Carlos da.
Series Studies in computational intelligence ; v. 1041.
Available in Other Form From Intervals To -?
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Intro
Preface
Contents
1 Motivation and Outline
1.1 Why Computers?
1.2 Why Interval Computations?
1.3 Why Go Beyond Intervals?
1.4 Outline
References
2 A General Description of Measuring Devices: Plan
3 A General Description of Measuring Devices: First Step-Finite Set of Possible Outcomes
3.1 Every Measuring Device Has Finitely Many Possible Outcomes
3.2 Not All Marks on a Scale Can Be Physically Possible
3.3 We Need a Theory
3.4 We Need a Theory that Also Described a Measuring Device
3.5 We Want a Theory that Is ``Full'' in Some Natural Sense

3.6 A Seemingly Natural Definition of a Full Theory is Not Always Adequate
3.7 What Exactly Is a Theory?
3.8 What Kind of Statements Are We Allowing?
3.9 What Exactly Is a Full Theory
3.10 The Existence of a Full Theory Makes the Set of All Physically ...
3.11 Conclusion: Algorithmically Listable Set of Physically Possible Outcomes
3.12 Example 1: Interval Uncertainty
3.13 Example 2: Counting
3.14 Example 3: ``Yes''-``No'' Measurements
3.15 Example 3a: Repeated ``Yes''-``No'' Measurements
3.16 Example 4: A Combination of Several Independent Measuring Instruments

4.9 Example 3: ``Yes''-``No'' Measurements
4.10 Example 3a: Repeated ``Yes''-``No'' Measurements
4.11 Example 4: A Combination of Several Independent Measuring Instruments
4.12 Computational Complexity of the Graph Representation of a Measuring Device: General Case
4.13 Computational Complexity of the Graph Representation of a Measuring Device: Case of the Simplest Interval Uncertainty
4.14 Computational Complexity of the Graph Representation of a Measuring Device: General Case of Interval Uncertainty

4.15 Computational Complexity of the Graph Representation of a Measuring Device: Lower Bound for the Case of the General Interval Uncertainty
4.16 Computational complexity of the Graph Representation of a Measuring Device: Case of Multi-D Uncertainty
4.17 Computational Complexity of the Graph Representation of a Measuring Device: General Case of Localized Uncertainty
References
5 A General Description of Measuring Devices: Third Step-Subsets of Compatible Outcomes
5.1 From Pairs to Subsets
5.2 Is Information About Compatible Pairs Sufficient?

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