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

Format:

Book

Author/Creator:

Kreinovich, Vladik, author.

Dimuro, Graçaliz Pereira, author.

Rocha Costa, Antônio Carlos da, author.

Series:

Studies in Computational Intelligence, 1860-9503 ; 1041

Language:

English

Subjects (All):

Computational intelligence.

Artificial intelligence.

Engineering--Data processing.

Engineering.

Computational Intelligence.

Artificial Intelligence.

Data Engineering.

Local Subjects:

Computational Intelligence.

Artificial Intelligence.

Data Engineering.

Physical Description:

1 online resource (125 pages)

Edition:

1st ed. 2023.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2023.

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 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 morecomplex 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.

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.

Notes:

Includes bibliographical references.

ISBN:

9783031205699

3031205693

OCLC:

1352970450