Measurement Uncertainty: An Approach via the Mathematical Theory of Evidence / Edition 1

by Simona Salicone

Overview

It is widely recognized, by the scientific and technical community that m- surements are the bridge between the empiric world and that of the abstract concepts and knowledge. In fact, measurements provide us the quantitative knowledge about things and phenomena. It is also widely recognized that the measurement result is capable of p- viding only incomplete information about the actual value of the measurand, that is, the quantity being measured. Therefore, a measurement result - comes useful, in any practicalsituation, only if a way is defined for estimating how incomplete is this information. The more recentdevelopment of measurement science has identified in the uncertainty concept the most suitable way to quantify how incomplete is the information provided by a measurement result. However, the problem of how torepresentameasurementresulttogetherwithitsuncertaintyandpropagate measurementuncertaintyisstillanopentopicinthe fieldofmetrology,despite many contributions that have been published in the literature over the years. Many problems are in fact still unsolved, starting from the identification of the best mathematical approach for representing incomplete knowledge. Currently, measurement uncertainty is treated in a purely probabilistic way, because the Theory of Probability has been considered the only available mathematical theory capable of handling incomplete information. However, this approach has the main drawback of requiring full compensation of any systematic effect that affects the measurement process. However, especially in many practical application, the identification and compensation of all systematic effects is not always possible or cost effective.

Product Details

ISBN-13:	9781441940346
Publisher:	Springer US
Publication date:	11/23/2010
Series:	Springer Series in Reliability Engineering
Edition description:	Softcover reprint of hardcover 1st ed. 2007
Pages:	228
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

Uncertainty in Measurement.- Fuzzy Variables and Measurement Uncertainty.- The Theory of Evidence.- Random-Fuzzy Variables.- Construction of Random-Fuzzy Variables.- Fuzzy Operators.- The Mathematics of Random-Fuzzy Variables.- Representation of Random-Fuzzy Variables.- Decision-Making Rules with Random-Fuzzy Variables.- List of Symbols.

Editorial Reviews

From the reviews:

"This book is the first to make full use of the mathematical theory of evidence to express the uncertainty in measurement. … This book can be useful for researchers (and practitioners) in the fields of statistics and measurement theory." (Robert Fuller, Mathematical Reviews, Issue 2007 j)

"This mathematics book is the first one to propose a different way of representing measurement uncertainty using fuzzy variables … . It is rare that a book of mathematics is so easy to read as this one, even for people unfamiliar with the topic of fuzzy variables. … The book is organised for and addressed to students … . It is also meant to be a ready-to-use tool for practitioners in measurements. … will interest researchers and specialists in the science of measurements." (Mariana Buzduga, International Journal of Acoustics and Vibration, Vol. 13 (1), 2008)

"The book under review is the first to make full use of this theory to express the uncertainly in measurements. … The book is designed for immediate use and applications in research and laboratory work in various fields, including applied probability, electrical and computer engineering, and experimental physics. Prerequisites for students include courses in statistics and measurement science." (Oleksandr Kukush, Zentralblatt MATH, Vol. 1144, 2008)

From the Publisher