Measurement Uncertainty

1. Front Matter

   Pages i-x

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2. Uncertainty in Measurement

   Pages 1-14

3. Fuzzy Variables and Measurement Uncertainty

   Pages 15-29

4. The Theory of Evidence

   Pages 31-71

5. Random-Fuzzy Variables

   Pages 73-85

6. Construction of Random-Fuzzy Variables

   Pages 87-98

7. Fuzzy Operators

   Pages 99-124

8. The Mathematics of Random-Fuzzy Variables

   Pages 125-194

9. Representation of Random-Fuzzy Variables

   Pages 195-196

10. Decision-Making Rules with Random-Fuzzy Variables

    Pages 197-222

11. List of Symbols

    Pages 223-224

12. Back Matter

    Pages 225-228

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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.

• Applied Mathematics
• Experiment
• Experimental Physics
• GUM
• Standard
• mathematics
• measurement
• uncertainty
• variable

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)

• Dipartimento di Elettrotecnica, Politecnico di Milano, Milano, Italy

  Simona Salicone

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