Fuzzy data in statistics

Milan Mareš

Kybernetika (2007)

  • Volume: 43, Issue: 4, page 491-502
  • ISSN: 0023-5954

Abstract

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The development of effective methods of data processing belongs to important challenges of modern applied mathematics and theoretical information science. If the natural uncertainty of the data means their vagueness, then the theory of fuzzy quantities offers relatively strong tools for their treatment. These tools differ from the statistical methods and this difference is not only justifiable but also admissible. This relatively brief paper aims to summarize the main fuzzy approaches to vague data processing, to discuss their main advantages and also their essential limitations, and to specify their place in the wide scale of information and knowledge processing methods effective for vague data.

How to cite

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Mareš, Milan. "Fuzzy data in statistics." Kybernetika 43.4 (2007): 491-502. <http://eudml.org/doc/33874>.

@article{Mareš2007,
abstract = {The development of effective methods of data processing belongs to important challenges of modern applied mathematics and theoretical information science. If the natural uncertainty of the data means their vagueness, then the theory of fuzzy quantities offers relatively strong tools for their treatment. These tools differ from the statistical methods and this difference is not only justifiable but also admissible. This relatively brief paper aims to summarize the main fuzzy approaches to vague data processing, to discuss their main advantages and also their essential limitations, and to specify their place in the wide scale of information and knowledge processing methods effective for vague data.},
author = {Mareš, Milan},
journal = {Kybernetika},
keywords = {fuzzy quantity; extension principle; fuzzy data; fuzzy quantities; extension principle},
language = {eng},
number = {4},
pages = {491-502},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Fuzzy data in statistics},
url = {http://eudml.org/doc/33874},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Mareš, Milan
TI - Fuzzy data in statistics
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 4
SP - 491
EP - 502
AB - The development of effective methods of data processing belongs to important challenges of modern applied mathematics and theoretical information science. If the natural uncertainty of the data means their vagueness, then the theory of fuzzy quantities offers relatively strong tools for their treatment. These tools differ from the statistical methods and this difference is not only justifiable but also admissible. This relatively brief paper aims to summarize the main fuzzy approaches to vague data processing, to discuss their main advantages and also their essential limitations, and to specify their place in the wide scale of information and knowledge processing methods effective for vague data.
LA - eng
KW - fuzzy quantity; extension principle; fuzzy data; fuzzy quantities; extension principle
UR - http://eudml.org/doc/33874
ER -

References

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  1. Dubois D., Prade H., Fuzzy numbers: An overview, In: Analysis of Fuzzy Information (J. C. Bezdek, ed.), Vol. 2, CRC-Press, Boca Raton 1988, pp. 3–39 (1988) MR0910312
  2. Dubois D., Kerre E. E., Mesiar, R., Prade H., 10.1007/978-1-4615-4429-6_11, In: Fundamental of Fuzzy Sets, Vol. 1, Kluwer Academic Publishers Kluwer Acad. Publ, Dodrecht 2000, pp. 483–581 Zbl0988.26020MR1890240DOI10.1007/978-1-4615-4429-6_11
  3. Kacprzyk J., (eds.) M. Fedrizi, Fuzzy Regression Analysis, Omnitech Press, Physica–Verlag, Warsaw 1992 MR1212587
  4. Kerre E. E., Wang X., Reasonable properties for the ordering of fuzzy quantities, Part I, Part II. Fuzzy Sets and Systems 118 (2001), 375–385, 387–405 Zbl0971.03055
  5. Klement E. P., Mesiar, R., Pap E., Triangular Norms, Kluwer Academic Publishers, Dordrecht 2000 Zbl1087.20041MR1790096
  6. Calvo T., Mayor, G., (eds.) R. Mesiar, Aggregation Operators, Physica–Verlag, Heidelberg 2002 Zbl0983.00020MR1936383
  7. Mareš M., Computation Over Fuzzy quantities, CRC–Press, Boca Raton 1994 Zbl0859.94035MR1327525
  8. Mareš M., 10.1016/S0165-0114(97)00136-X, Fuzzy Sets and Systems 91 (1997), 2, 143–154 (1997) MR1480041DOI10.1016/S0165-0114(97)00136-X
  9. Mareš M., Mesiar R., Verbally generated fuzzy quantities and their aggregation, In: Analysis of Fuzzy Information (J. C. Bezdek, ed.), Vol. 2, CRC-Press, Boca Raton 1988, pp. 291–3352 (1988) MR1936394
  10. Mareš M., Mesiar R., Dual meaning of verbal quantities, Kybernetika 38 (2002), 6, 709–716 MR1954392
  11. Chien, Tran Quoc, Medium distances of probability fuzzy-points and an application to linear programming, Kybernetika 25 (1989), 6, 494–504 (1989) Zbl0715.90074MR1035154
  12. Zadeh L. A., 10.1016/S0019-9958(65)90241-X, Inform. and Control 8 (1965), 3, 338–353 (1965) Zbl0139.24606MR0219427DOI10.1016/S0019-9958(65)90241-X

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