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From intervals to -?towards a general description of validated uncertainty /

Record Type:	Electronic resources : Monograph/item
Title/Author:	From intervals to -?by Vladik Kreinovich, Graçaliz Pereira Dimuro, Antônio Carlos da Rocha Costa.
Reminder of title:	towards a general description of validated uncertainty /
Author:	Kreinovich, Vladik.
other author:	Dimuro, Graçaliz Pereira.
Published:	Cham :Springer International Publishing :2023.
Description:	xiii, 116 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Uncertainty (Information theory)
Online resource:	https://doi.org/10.1007/978-3-031-20569-9
ISBN:	9783031205699$q(electronic bk.)

From intervals to -?towards a general description of validated uncertainty /
Kreinovich, Vladik.

From intervals to -?towards a general description of validated uncertainty /[electronic resource] :by Vladik Kreinovich, Graçaliz Pereira Dimuro, Antônio Carlos da Rocha Costa. - Cham :Springer International Publishing :2023. - xiii, 116 p. :ill., digital ;24 cm. - Studies in computational intelligence,v. 10411860-9503 ;. - Studies in computational intelligence ;v. 216..

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.

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 result-as computers do-with 13 digit accuracy. In many cases-e.g., in celestial mechanics-the 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 instrument-or 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 methodology-a 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.

ISBN: 9783031205699$q(electronic bk.)

Standard No.: 10.1007/978-3-031-20569-9doiSubjects--Topical Terms:

206405
Uncertainty (Information theory)

LC Class. No.: Q375

Dewey Class. No.: 003.54

From intervals to -?towards a general description of validated uncertainty /
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520 $a 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 result-as computers do-with 13 digit accuracy. In many cases-e.g., in celestial mechanics-the 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 instrument-or 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 methodology-a 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.
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