Theoretical prerequisites for implementation of metrological self-tracking of measurement data analysis programs

Semenov, Konstantin K.; Solopchenko, G. N.

doi:10.1007/s11018-010-9547-1

Cited by 2 publications

(1 citation statement)

References 6 publications

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“…For this, it is proposed to use combination of fuzzy interval formalism and automatic differentiation technique. Realization of this approach requires very small modifications in software initial code [21].…”

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confidence: 99%

Fuzzy Intervals as Foundation of Metrological Support for Computations With Inaccurate Data

Semenov¹,

Solopchenko²,

Kreinovich³

2015

Series on Advances in Mathematics for Applied Sciences

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In this paper, we discuss the possibility of using the formalism of fuzzy intervals combined with automatic differentiation technique as a basis for numerical software selfverification in metrology. The natural domain of such approach is calculating indirect measurements results using the inaccurate results of direct measurements as the initial data. We propose to support software for such computations with tools that allow us to receive simultaneously calculated results and their error characteristics. Only such software can be put to metrological validation in full.In many practical situations, the inaccurate results of direct measurements are used for calculations of indirect measurements results. Final data are also uncertain. Characteristics of this uncertainty should be expressed in quantitative form and presented together with indirect measurement result. The main purpose of this paper is to discuss ways to provide software for measured data processing with tools of automatic calculation of final result uncertainty. Only software that is supported in such manner can pass the metrological certification in full.To achieve this purpose, we propose to use combination of two formalisms: fuzzy intervals approach -to represent inaccuracy of initial data for calculations, and formalism of software automatic differentiation -to compute how initial data uncertainty transforms to inherited uncertainty of final result.There are many approaches for representing inaccuracy of measured data that act as initial information for subsequent calculations. Modern approaches take into account different information about the initial data inaccuracy. Some of them use random variables [1][2][3] for uncertainty representing and handling with it, other ones use bounds on possible values of initial data [4][5][6]. Interval representation of data inaccuracy was firstly mentioned by Wiener [7] and Kantorovich [8]. With the development of the fuzzy set theory, its formalism became actual tool for uncertainty expressing in metrology [9,10]. Natural evolution of ideas of interval and fuzzy frameworks is the concept of fuzzy

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Fuzzy Intervals as Foundation of Metrological Support for Computations With Inaccurate Data

Semenov¹,

Solopchenko²,

Kreinovich³

2015

Series on Advances in Mathematics for Applied Sciences

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The metrologically reasonable clustering of measurement results

Semenov

Bolschikov

2019

J. Phys.: Conf. Ser.

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This paper is dedicated to the metrological aspects of clustering procedure. It is shown that taking into account the information on uncertainty of the data to be clustered allows easily making reasonable decisions that are metrologically supported. The paper presents that the problems that are usually difficult to solve in practice of the clustering become simpler: the proposed approach allows determining the number of maximum recognizable clusters and thus protects from the unreasonable conclusions and allows performing the preconditioning of data to be clustered simpler.

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Theoretical prerequisites for implementation of metrological self-tracking of measurement data analysis programs

Cited by 2 publications

References 6 publications

Fuzzy Intervals as Foundation of Metrological Support for Computations With Inaccurate Data

Fuzzy Intervals as Foundation of Metrological Support for Computations With Inaccurate Data

The metrologically reasonable clustering of measurement results

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