Homogeneous aggregation operators

Tatiana Rückschlossová; Roman Rückschloss

Kybernetika (2006)

  • Volume: 42, Issue: 3, page 279-286
  • ISSN: 0023-5954

Abstract

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Recently, the utilization of invariant aggregation operators, i.e., aggregation operators not depending on a given scale of measurement was found as a very current theme. One type of invariantness of aggregation operators is the homogeneity what means that an aggregation operator is invariant with respect to multiplication by a constant. We present here a complete characterization of homogeneous aggregation operators. We discuss a relationship between homogeneity, kernel property and shift-invariance of aggregation operators. Several examples are included.

How to cite

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Rückschlossová, Tatiana, and Rückschloss, Roman. "Homogeneous aggregation operators." Kybernetika 42.3 (2006): 279-286. <http://eudml.org/doc/33805>.

@article{Rückschlossová2006,
abstract = {Recently, the utilization of invariant aggregation operators, i.e., aggregation operators not depending on a given scale of measurement was found as a very current theme. One type of invariantness of aggregation operators is the homogeneity what means that an aggregation operator is invariant with respect to multiplication by a constant. We present here a complete characterization of homogeneous aggregation operators. We discuss a relationship between homogeneity, kernel property and shift-invariance of aggregation operators. Several examples are included.},
author = {Rückschlossová, Tatiana, Rückschloss, Roman},
journal = {Kybernetika},
keywords = {aggregation operator; homogeneity; kernel property; aggregation operator; homogeneity; kernel property},
language = {eng},
number = {3},
pages = {279-286},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Homogeneous aggregation operators},
url = {http://eudml.org/doc/33805},
volume = {42},
year = {2006},
}

TY - JOUR
AU - Rückschlossová, Tatiana
AU - Rückschloss, Roman
TI - Homogeneous aggregation operators
JO - Kybernetika
PY - 2006
PB - Institute of Information Theory and Automation AS CR
VL - 42
IS - 3
SP - 279
EP - 286
AB - Recently, the utilization of invariant aggregation operators, i.e., aggregation operators not depending on a given scale of measurement was found as a very current theme. One type of invariantness of aggregation operators is the homogeneity what means that an aggregation operator is invariant with respect to multiplication by a constant. We present here a complete characterization of homogeneous aggregation operators. We discuss a relationship between homogeneity, kernel property and shift-invariance of aggregation operators. Several examples are included.
LA - eng
KW - aggregation operator; homogeneity; kernel property; aggregation operator; homogeneity; kernel property
UR - http://eudml.org/doc/33805
ER -

References

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  10. Lázaro J., Rückschlossová, T., Calvo T., 10.1016/j.fss.2003.10.031, Fuzzy Sets and Systems 142 (2004), 51–62 Zbl1081.68106MR2045342DOI10.1016/j.fss.2003.10.031
  11. Mesiar R., Rückschlossová T., 10.1016/j.fss.2003.10.032, Fuzzy Sets and Systems 142 (2004), 63–73 Zbl1049.68133MR2045343DOI10.1016/j.fss.2003.10.032
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