### Synopses & Reviews

The expression of uncertainty in measurement is a challenging aspect for researchers and engineers working in instrumentation and measurement because it involves physical, mathematical and philosophical issues. This problem is intensified by the limitations of the probabilistic approach used by the current standard (GUM). This text is the first to make full use of the mathematical theory of evidence to express the uncertainty in measurements. It gives an overview of the current standard, then pinpoints and constructively resolves its limitations through its unique approach. The text presents various tools for evaluating uncertainty, beginning with the probabilistic approach and concluding with the expression of uncertainty using random-fuzzy variables. The exposition is driven by numerous examples. The book is designed for immediate use and application in research and laboratory work. Prerequisites for students include courses in statistics and measurement science. Apart from a classroom setting, this book can be used by practitioners in a variety of fields (including applied mathematics, applied probability, electrical and computer engineering, and experimental physics), and by such institutions as the IEEE, ISA, and National Institute of Standards and Technology.

#### Review

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)

#### Synopsis

It is widely recognized, by the scienti?c 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 de?ned for estimating how incomplete is this information. The more recentdevelopment of measurement science has identi?ed 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?eldofmetrology, despite many contributions that have been published in the literature over the years. Many problems are in fact still unsolved, starting from the identi?cation 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 e?ect that a?ects the measurement process. However, especially in many practical application, the identi?cation and compensation of all s- tematic e?ects is not always possible or cost e?ective

#### Synopsis

The expression of uncertainty in measurement is a challenging aspect for researchers and engineers working in instrumentation and measurement because it involves physical, mathematical and philosophical issues. This problem is intensified by the limitations of the probabilistic approach used by the current standard (GUM).

This text is the first to make full use of the mathematical theory of evidence to express the uncertainty in measurements. It gives an overview of the current standard, then pinpoints and constructively resolves its limitations through its unique approach. The text presents various tools for evaluating uncertainty, beginning with the probabilistic approach and concluding with the expression of uncertainty using random-fuzzy variables. The exposition is driven by numerous examples. The book is designed for immediate use and application in research and laboratory work.

Apart from a classroom setting, this book can be used by practitioners in a variety of fields (including applied mathematics, applied probability, electrical and computer engineering, and experimental physics), and by such institutions as the IEEE, ISA, and National Institute of Standards and Technology.

#### Synopsis

This book presents an alternative approach and companion to the GUM Instrumentation Standard. Coverage provides an overview of the current standard, then pinpoints and constructively resolves its limitations.

#### Synopsis

The expression of uncertainty in measurement poses a challenge since it involves physical, mathematical, and philosophical issues. This problem is intensified by the limitations of the probabilistic approach used by the current standard (the GUM Instrumentation Standard). This text presents an alternative approach. It makes full use of the mathematical theory of evidence to express the uncertainty in measurements. Coverage provides an overview of the current standard, then pinpoints and constructively resolves its limitations. Numerous examples throughout help explain the book's unique approach.

### Table of Contents

Preface.- 1. Uncertainty in Measurement.- 2. Fuzzy Variables and Measurement Uncertainty.- 3. The Theory of Evidence.- 4. Random-Fuzzy Variables.- 5. Construction of Random-Fuzzy Variables.- 6. Fuzzy Operators.- 7. The Mathematics of Random-Fuzzy Variables.- 8. Representation of Random-Fuzzy Variables.- 9. Decision-Making Rules with Random-Fuzzy Variables.- 10. List of Symbols.- Bibliography.- Index.