Möbius fitting aggregation operators

Anna Kolesárová

Kybernetika (2002)

  • Volume: 38, Issue: 3, page [259]-273
  • ISSN: 0023-5954

Abstract

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Standard Möbius transform evaluation formula for the Choquet integral is associated with the 𝐦𝐢𝐧 -aggregation. However, several other aggregation operators replacing 𝐦𝐢𝐧 operator can be applied, which leads to a new construction method for aggregation operators. All binary operators applicable in this approach are characterized by the 1-Lipschitz property. Among ternary aggregation operators all 3-copulas are shown to be fitting and moreover, all fitting weighted means are characterized. This new method allows to construct aggregation operators from simpler ones.

How to cite

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Kolesárová, Anna. "Möbius fitting aggregation operators." Kybernetika 38.3 (2002): [259]-273. <http://eudml.org/doc/33581>.

@article{Kolesárová2002,
abstract = {Standard Möbius transform evaluation formula for the Choquet integral is associated with the $\mathbf \{min\}$-aggregation. However, several other aggregation operators replacing $\mathbf \{min\}$ operator can be applied, which leads to a new construction method for aggregation operators. All binary operators applicable in this approach are characterized by the 1-Lipschitz property. Among ternary aggregation operators all 3-copulas are shown to be fitting and moreover, all fitting weighted means are characterized. This new method allows to construct aggregation operators from simpler ones.},
author = {Kolesárová, Anna},
journal = {Kybernetika},
keywords = {aggregation operator; Choquet integral; aggregation operator; Choquet integral},
language = {eng},
number = {3},
pages = {[259]-273},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Möbius fitting aggregation operators},
url = {http://eudml.org/doc/33581},
volume = {38},
year = {2002},
}

TY - JOUR
AU - Kolesárová, Anna
TI - Möbius fitting aggregation operators
JO - Kybernetika
PY - 2002
PB - Institute of Information Theory and Automation AS CR
VL - 38
IS - 3
SP - [259]
EP - 273
AB - Standard Möbius transform evaluation formula for the Choquet integral is associated with the $\mathbf {min}$-aggregation. However, several other aggregation operators replacing $\mathbf {min}$ operator can be applied, which leads to a new construction method for aggregation operators. All binary operators applicable in this approach are characterized by the 1-Lipschitz property. Among ternary aggregation operators all 3-copulas are shown to be fitting and moreover, all fitting weighted means are characterized. This new method allows to construct aggregation operators from simpler ones.
LA - eng
KW - aggregation operator; Choquet integral; aggregation operator; Choquet integral
UR - http://eudml.org/doc/33581
ER -

References

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