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M-estimates of location for the robust central tendency of fuzzy data

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Abstract
The Aumann-type mean has been shown to possess valuable properties as a measure of the location or central tendency of fuzzy data associated with a random experiment. However, concerning robustness its behavior is not appropriate. The Aumann-type mean is highly affected by slight changes in the fuzzy data or when outliers arise in the sample. Robust estimators of location, on the other hand, avoid such adverse effects. For this purpose, this paper considers the M-estimation approach and discusses conditions under which this alternative yields valid fuzzy-valued M-estimators. The resulting M-estimators are applied to a real-life example. Finally, some simulation studies show-empirically the suitability of the introduced estimators.
Keywords
LINGUISTIC TERM SETS, NUMBER-VALUED DATA, TRAPEZOIDAL APPROXIMATIONS, STATISTICAL-ANALYSIS, RANDOM-VARIABLES, RATING-SCALE, PARAMETER, SUPPORT, Fuzzy number-valued data, M-estimators, random fuzzy numbers, robust, location of fuzzy data

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Citation

Please use this url to cite or link to this publication:

Chicago
Sinova, Beatriz, María Ángeles Gil, and Stefan Van Aelst. 2016. “M-estimates of Location for the Robust Central Tendency of Fuzzy Data.” Ieee Transactions on Fuzzy Systems 24 (4): 945–956.
APA
Sinova, B., Ángeles Gil, M., & Van Aelst, S. (2016). M-estimates of location for the robust central tendency of fuzzy data. IEEE TRANSACTIONS ON FUZZY SYSTEMS, 24(4), 945–956.
Vancouver
1.
Sinova B, Ángeles Gil M, Van Aelst S. M-estimates of location for the robust central tendency of fuzzy data. IEEE TRANSACTIONS ON FUZZY SYSTEMS. 2016;24(4):945–56.
MLA
Sinova, Beatriz, María Ángeles Gil, and Stefan Van Aelst. “M-estimates of Location for the Robust Central Tendency of Fuzzy Data.” IEEE TRANSACTIONS ON FUZZY SYSTEMS 24.4 (2016): 945–956. Print.
@article{8513248,
  abstract     = {The Aumann-type mean has been shown to possess valuable properties as a measure of the location or central tendency of fuzzy data associated with a random experiment. However, concerning robustness its behavior is not appropriate. The Aumann-type mean is highly affected by slight changes in the fuzzy data or when outliers arise in the sample. Robust estimators of location, on the other hand, avoid such adverse effects. For this purpose, this paper considers the M-estimation approach and discusses conditions under which this alternative yields valid fuzzy-valued M-estimators. The resulting M-estimators are applied to a real-life example. Finally, some simulation studies show-empirically the suitability of the introduced estimators.},
  author       = {Sinova, Beatriz and {\'A}ngeles Gil, Mar{\'i}a and Van Aelst, Stefan},
  issn         = {1063-6706},
  journal      = {IEEE TRANSACTIONS ON FUZZY SYSTEMS},
  language     = {eng},
  number       = {4},
  pages        = {945--956},
  title        = {M-estimates of location for the robust central tendency of fuzzy data},
  url          = {http://dx.doi.org/10.1109/TFUZZ.2015.2489245},
  volume       = {24},
  year         = {2016},
}

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