From Intervals to -? [electronic resource] : Towards a General Description of Validated Uncertainty / by Vladik Kreinovich, Graçaliz Pereira Dimuro, Antônio Carlos da Rocha Costa.

Por: Kreinovich, Vladik [author.]Colaborador(es): Dimuro, Graçaliz Pereira [author.] | da Rocha Costa, Antônio Carlos [author.] | SpringerLink (Online service)Tipo de material: TextoTextoSeries Studies in Computational Intelligence ; 1041Editor: Cham : Springer International Publishing : Imprint: Springer, 2023Edición: 1st ed. 2023Descripción: XIII, 116 p. 26 illus. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783031205699Tema(s): Computational intelligence | Artificial intelligence | Engineering -- Data processing | Computational Intelligence | Artificial Intelligence | Data EngineeringFormatos físicos adicionales: Printed edition:: Sin título; Printed edition:: Sin título; Printed edition:: Sin títuloClasificación CDD: 006.3 Clasificación LoC:Q342Recursos en línea: Libro electrónicoTexto
Contenidos:
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.
En: Springer Nature eBookResumen: 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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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.

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