Aggregations preserving classes of fuzzy relations

Józef Drewniak; Urszula Dudziak

Kybernetika (2005)

  • Volume: 41, Issue: 3, page [265]-284
  • ISSN: 0023-5954

Abstract

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We consider aggregations of fuzzy relations using means in [0,1] (especially: minimum, maximum and quasilinear mean). After recalling fundamental properties of fuzzy relations we examine means, which preserve reflexivity, symmetry, connectedness and transitivity of fuzzy relations. Conversely, some properties of aggregated relations can be inferred from properties of aggregation results. Results of the paper are completed by suitable examples and counter- examples, which is summarized in a special table at the end of the paper.

How to cite

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Drewniak, Józef, and Dudziak, Urszula. "Aggregations preserving classes of fuzzy relations." Kybernetika 41.3 (2005): [265]-284. <http://eudml.org/doc/33753>.

@article{Drewniak2005,
abstract = {We consider aggregations of fuzzy relations using means in [0,1] (especially: minimum, maximum and quasilinear mean). After recalling fundamental properties of fuzzy relations we examine means, which preserve reflexivity, symmetry, connectedness and transitivity of fuzzy relations. Conversely, some properties of aggregated relations can be inferred from properties of aggregation results. Results of the paper are completed by suitable examples and counter- examples, which is summarized in a special table at the end of the paper.},
author = {Drewniak, Józef, Dudziak, Urszula},
journal = {Kybernetika},
keywords = {fuzzy relation; reflexivity; symmetry; connectedness; $\star $-transitivity; transitivity; weak property; relation aggregation; mean; arithmetic mean; quasi-arithmetic mean; quasilinear mean; weighted average; fuzzy relation; reflexivity; symmetry; connectedness; -transitivity; relation aggregation; quasi-arithmetic mean; quasilinear mean},
language = {eng},
number = {3},
pages = {[265]-284},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Aggregations preserving classes of fuzzy relations},
url = {http://eudml.org/doc/33753},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Drewniak, Józef
AU - Dudziak, Urszula
TI - Aggregations preserving classes of fuzzy relations
JO - Kybernetika
PY - 2005
PB - Institute of Information Theory and Automation AS CR
VL - 41
IS - 3
SP - [265]
EP - 284
AB - We consider aggregations of fuzzy relations using means in [0,1] (especially: minimum, maximum and quasilinear mean). After recalling fundamental properties of fuzzy relations we examine means, which preserve reflexivity, symmetry, connectedness and transitivity of fuzzy relations. Conversely, some properties of aggregated relations can be inferred from properties of aggregation results. Results of the paper are completed by suitable examples and counter- examples, which is summarized in a special table at the end of the paper.
LA - eng
KW - fuzzy relation; reflexivity; symmetry; connectedness; $\star $-transitivity; transitivity; weak property; relation aggregation; mean; arithmetic mean; quasi-arithmetic mean; quasilinear mean; weighted average; fuzzy relation; reflexivity; symmetry; connectedness; -transitivity; relation aggregation; quasi-arithmetic mean; quasilinear mean
UR - http://eudml.org/doc/33753
ER -

References

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