Preservation of properties of fuzzy relations during aggregation processes

Józef Drewniak; Urszula Dudziak

Kybernetika (2007)

  • Volume: 43, Issue: 2, page 115-132
  • ISSN: 0023-5954

Abstract

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Diverse classes of fuzzy relations such as reflexive, irreflexive, symmetric, asymmetric, antisymmetric, connected, and transitive fuzzy relations are studied. Moreover, intersections of basic relation classes such as tolerances, tournaments, equivalences, and orders are regarded and the problem of preservation of these properties by n -ary operations is considered. Namely, with the use of fuzzy relations R 1 , ... , R n and n -argument operation F on the interval [ 0 , 1 ] , a new fuzzy relation R F = F ( R 1 , ... , R n ) is created. Characterization theorems concerning the problem of preservation of fuzzy relations properties are given. Some conditions on aggregation functions are weakened in comparison to those previously given by other authors.

How to cite

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Drewniak, Józef, and Dudziak, Urszula. "Preservation of properties of fuzzy relations during aggregation processes." Kybernetika 43.2 (2007): 115-132. <http://eudml.org/doc/33846>.

@article{Drewniak2007,
abstract = {Diverse classes of fuzzy relations such as reflexive, irreflexive, symmetric, asymmetric, antisymmetric, connected, and transitive fuzzy relations are studied. Moreover, intersections of basic relation classes such as tolerances, tournaments, equivalences, and orders are regarded and the problem of preservation of these properties by $n$-ary operations is considered. Namely, with the use of fuzzy relations $R_1,\ldots ,R_n$ and $n$-argument operation $F$ on the interval $[0,1]$, a new fuzzy relation $R_F=F(R_1,\ldots ,R_n)$ is created. Characterization theorems concerning the problem of preservation of fuzzy relations properties are given. Some conditions on aggregation functions are weakened in comparison to those previously given by other authors.},
author = {Drewniak, Józef, Dudziak, Urszula},
journal = {Kybernetika},
keywords = {fuzzy relation; fuzzy relation properties; fuzzy relation classes; $\ast $-transitivity; transitivity; aggregation functions; relation aggregation; triangular norms; Fuzzy relation; Classes of fuzzy relations; Transitivity; Aggregation function; Relation aggregation; Triangular norm},
language = {eng},
number = {2},
pages = {115-132},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Preservation of properties of fuzzy relations during aggregation processes},
url = {http://eudml.org/doc/33846},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Drewniak, Józef
AU - Dudziak, Urszula
TI - Preservation of properties of fuzzy relations during aggregation processes
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 2
SP - 115
EP - 132
AB - Diverse classes of fuzzy relations such as reflexive, irreflexive, symmetric, asymmetric, antisymmetric, connected, and transitive fuzzy relations are studied. Moreover, intersections of basic relation classes such as tolerances, tournaments, equivalences, and orders are regarded and the problem of preservation of these properties by $n$-ary operations is considered. Namely, with the use of fuzzy relations $R_1,\ldots ,R_n$ and $n$-argument operation $F$ on the interval $[0,1]$, a new fuzzy relation $R_F=F(R_1,\ldots ,R_n)$ is created. Characterization theorems concerning the problem of preservation of fuzzy relations properties are given. Some conditions on aggregation functions are weakened in comparison to those previously given by other authors.
LA - eng
KW - fuzzy relation; fuzzy relation properties; fuzzy relation classes; $\ast $-transitivity; transitivity; aggregation functions; relation aggregation; triangular norms; Fuzzy relation; Classes of fuzzy relations; Transitivity; Aggregation function; Relation aggregation; Triangular norm
UR - http://eudml.org/doc/33846
ER -

References

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