A general mathematical approach to represent measurement results
LECTURER
Simona Salicone
Politecnico di Milano, Italy
ABSTRACT
The mathematical theory of possibility will be presented as an alternative, though not conflicting
mathematical approach to probability theory for the expression, evaluation and propagation of
measurement uncertainty.
Thanks to the definition of some variables, called Random-Fuzzy variables, this theory yields a unique
mathematical representation of all kinds of uncertainty contributions. The Random-Fuzzy variable
represents in fact a measurement result and all associated measurement uncertainty contributions: the
random contributions to uncertainty, the unknown systematic contributions, and the uncompensated
systematic contributions. Furthermore, under this mathematical framework, the combination of
measurement results is mathematically done by combining Random-Fuzzy variables and, thanks to the
availability of different operators (t-norms), each contribution can be combined in the most appropriate
way, according to the way they affect the measurement procedure.
Some examples will be provided, and it will be shown how this mathematics can effectively represent some
of the most common situations in metrology (including the so-called total ignorance) and propagate all
kinds of uncertainty contributions properly according to all the available metrological information.
SHORT BIOGRAPHY
Simona Salicone is an Associate Professor of electrical and electronic
measurements at Dipartimento di Elettronica, Informazione e
Bioingegneria (DEIB), Politecnico di Milano.
Her principal research interests are concerned with the analysis of
advanced mathematical methods for uncertainty representation and
estimation. Her research activity is reflected in the over 100 papers
published in international and national scientific journals, in the
proceedings of national and international conferences in the field of
instrumentation and measurements, and in two monographs, edited by Springer: “Measurement
Uncertainty. An approach via the mathematical theory of evidence” (2007) and “Measuring
Uncertainty within the Theory of Evidence” (2018).
In 2004 she has received, by the IEEE Instrumentation and Measurement Society, in recognition of
contributions made to measurement uncertainty theory, the 2004 Outstanding Young Engineer
Award. In 2007, Simona Salicone is elected, by the Officers and Board of Directors of the IEEE, to
the grade of IEEE Senior Member. In years 2013 to 2017, Simona Salicone has been part of the
Academic Board of the PhD in Electrical Engineering at Politecnico di Milano. Since 2014
until the end of 2016, she has been part of the Editorial Board of the IEEE Instrumentation and
Measurement Magazine, as the responsible of the column “Future Trends in Instrumentation &
Measurements”. Since January 2016 until the end of 2017, Simona Salicone has been the Associate
Editor in Chief of the IEEE Instrumentation and Measurement Magazine. In 2016 Simona
Salicone has received, in appreciation of outstanding service to IEEE Transaction on
Instrumentation and Measurement, the recognition as one of the Transactions Outstanding
Reviewers of 2015, by the IEEE Instrumentation and Measurement Society. Simona Salicone is the
winner of the 2016 IEEE Instrumentation and Measurement Society Faculty Course
Development Award.
In 2019, her monograph “Measuring Uncertainty within the Theory of Evidence” was among the
top 25% most downloaded eBooks in its respective eBook Collection. In 2020, Simona Salicone
has been recognized as a Top 70 Most Published Author of All Time by the IEEE
Instrumentation and Measurement Society – Transaction on Instrumentation and Measurement.
Since 2019, Simona is part of the Selection Committee of the IEEE Faculty Course Development
Award. Since 2021, she has been part of the Editorial Board of the MDPI Metrology journal.