Weighted means and weighting functions

Radko Mesiar; Jana Špirková

Kybernetika (2006)

  • Volume: 42, Issue: 2, page 151-160
  • ISSN: 0023-5954

Abstract

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We present some properties of mixture and generalized mixture operators, with special stress on their monotonicity. We introduce new sufficient conditions for weighting functions to ensure the monotonicity of the corresponding operators. However, mixture operators, generalized mixture operators neither quasi-arithmetic means weighted by a weighting function need not be non- decreasing operators, in general.

How to cite

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Mesiar, Radko, and Špirková, Jana. "Weighted means and weighting functions." Kybernetika 42.2 (2006): 151-160. <http://eudml.org/doc/33798>.

@article{Mesiar2006,
abstract = {We present some properties of mixture and generalized mixture operators, with special stress on their monotonicity. We introduce new sufficient conditions for weighting functions to ensure the monotonicity of the corresponding operators. However, mixture operators, generalized mixture operators neither quasi-arithmetic means weighted by a weighting function need not be non- decreasing operators, in general.},
author = {Mesiar, Radko, Špirková, Jana},
journal = {Kybernetika},
keywords = {mixture operator; generalized mixture operator; monotonicity of the mixture operator; quasi-arithmetic mean; ordinal approach; generalized mixture operator; monotonicity; quasi-arithmetic mean; ordinal approach},
language = {eng},
number = {2},
pages = {151-160},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Weighted means and weighting functions},
url = {http://eudml.org/doc/33798},
volume = {42},
year = {2006},
}

TY - JOUR
AU - Mesiar, Radko
AU - Špirková, Jana
TI - Weighted means and weighting functions
JO - Kybernetika
PY - 2006
PB - Institute of Information Theory and Automation AS CR
VL - 42
IS - 2
SP - 151
EP - 160
AB - We present some properties of mixture and generalized mixture operators, with special stress on their monotonicity. We introduce new sufficient conditions for weighting functions to ensure the monotonicity of the corresponding operators. However, mixture operators, generalized mixture operators neither quasi-arithmetic means weighted by a weighting function need not be non- decreasing operators, in general.
LA - eng
KW - mixture operator; generalized mixture operator; monotonicity of the mixture operator; quasi-arithmetic mean; ordinal approach; generalized mixture operator; monotonicity; quasi-arithmetic mean; ordinal approach
UR - http://eudml.org/doc/33798
ER -

References

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  12. Ribeiro R. A., Pereira R. A. M., Aggregation with generalized mixture operators using weighting functions, Fuzzy Sets and Systems 137 (2003), 43–58 Zbl1041.91024MR1992697
  13. Pereira R. A. M., Pasi G., On non-monotonic aggregation: Mixture operators, In: Proc. 4th Meeting of the EURO Working Group on Fuzzy Sets (EUROFUSE’99) and 2nd Internat. Conference on Soft and Intelligent Computing (SIC’99), Budapest 1999 
  14. Ribeiro R. A., Pereira R. A. M., Weights as functions of attribute satisfaction values, In: Proc. Workshop on Preference Modelling and Applications (EUROFUSE), Granada 2001 
  15. Ribeiro R. A., Pereira R. A. M., 10.1016/S0377-2217(02)00538-6, European J. Oper. Res. 145 (2003), 329–342 Zbl1011.90504DOI10.1016/S0377-2217(02)00538-6
  16. Yager R. R., 10.1109/21.87068, IEEE Trans. Systems Man Cybernet. 18 (1988), 183–190 (1988) MR0931863DOI10.1109/21.87068

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