On the description and analysis of measurements of continuous quantities

Reinhard Viertl

Kybernetika (2002)

  • Volume: 38, Issue: 3, page [353]-362
  • ISSN: 0023-5954

Abstract

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The measurement of continuous quantities is the basis for all mathematical and statistical analysis of phenomena in engineering and science.Therefore a suitable mathematical description of measurement results is basic for realistic analysis methods for such data. Since the result of a measurement of a continuous quantity is not a precise real number but more or less non- precise, it is necessary to use an appropriate mathematical concept to describe measurements. This is possible by the description of a measurement result by a so-called non-precise number. A non-precise number is a generalization of a real number and is defined by a so-called characterizing function. In case of vector valued quantities the concept of so-called non- precise vectors can be used. Based on these concepts more realistic data analysis methods for measurement data are possible.

How to cite

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Viertl, Reinhard. "On the description and analysis of measurements of continuous quantities." Kybernetika 38.3 (2002): [353]-362. <http://eudml.org/doc/33588>.

@article{Viertl2002,
abstract = {The measurement of continuous quantities is the basis for all mathematical and statistical analysis of phenomena in engineering and science.Therefore a suitable mathematical description of measurement results is basic for realistic analysis methods for such data. Since the result of a measurement of a continuous quantity is not a precise real number but more or less non- precise, it is necessary to use an appropriate mathematical concept to describe measurements. This is possible by the description of a measurement result by a so-called non-precise number. A non-precise number is a generalization of a real number and is defined by a so-called characterizing function. In case of vector valued quantities the concept of so-called non- precise vectors can be used. Based on these concepts more realistic data analysis methods for measurement data are possible.},
author = {Viertl, Reinhard},
journal = {Kybernetika},
keywords = {non-precise data; hypothesis testing; non-precise data; hypothesis testing},
language = {eng},
number = {3},
pages = {[353]-362},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On the description and analysis of measurements of continuous quantities},
url = {http://eudml.org/doc/33588},
volume = {38},
year = {2002},
}

TY - JOUR
AU - Viertl, Reinhard
TI - On the description and analysis of measurements of continuous quantities
JO - Kybernetika
PY - 2002
PB - Institute of Information Theory and Automation AS CR
VL - 38
IS - 3
SP - [353]
EP - 362
AB - The measurement of continuous quantities is the basis for all mathematical and statistical analysis of phenomena in engineering and science.Therefore a suitable mathematical description of measurement results is basic for realistic analysis methods for such data. Since the result of a measurement of a continuous quantity is not a precise real number but more or less non- precise, it is necessary to use an appropriate mathematical concept to describe measurements. This is possible by the description of a measurement result by a so-called non-precise number. A non-precise number is a generalization of a real number and is defined by a so-called characterizing function. In case of vector valued quantities the concept of so-called non- precise vectors can be used. Based on these concepts more realistic data analysis methods for measurement data are possible.
LA - eng
KW - non-precise data; hypothesis testing; non-precise data; hypothesis testing
UR - http://eudml.org/doc/33588
ER -

References

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  1. Bandemer H., Näther W., Fuzzy Data Analysis, Kluwer, Dordrecht 1992 Zbl0758.62003MR1175172
  2. Dubois D., Kerre E., Mesiar R., Prade H., Fuzzy Interval Analysis, In: Fundamentals of Fuzzy Sets (D. Dubois, H. Prade, eds.), Kluwer, Boston 2000 Zbl0988.26020MR1890240
  3. Klir G., Yuan B., Fuzzy Sets and Fuzzy Logic – Theory and Applications, Prentice Hall, Upper Saddle River, N.J. 1995 Zbl0915.03001MR1329731
  4. Menger K., Ensembles flous et fonctions aléatoires, Comptes Rendus Acad, Sci. 232 (1951), 2001–2003 (1951) MR0042082
  5. Nguyen H., 10.1016/0022-247X(78)90045-8, Math. Anal. Appl. 64 (1978), 369–380 (1978) MR0480044DOI10.1016/0022-247X(78)90045-8
  6. Viertl R., Statistical Methods for Non–Precise Data, CRC Press, Boca Raton 1996 Zbl0853.62004MR1382865
  7. Viertl R., Non–Precise Data (Encyclopedia Math, , Suppl. II). Kluwer, Dordrecht 2000 
  8. Viertl R., Statistical Inference with Non-Precise Data, In: Encyclopedia of Life Support Systems, UNESCO, Paris, to appear on-line 
  9. Zadeh L., 10.1016/S0019-9958(65)90241-X, Information and Control 8 (1965), 338–353 (1965) Zbl0139.24606MR0219427DOI10.1016/S0019-9958(65)90241-X
  10. Zadeh L., The concept of a linguistic variable and its applications to approximate reasoning, Parts I, II, III. Inform. Sci. 8 (1975), 199–249 (1975) MR0386369

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