Geodesic
Preservation of properties of fuzzy relations during aggregation processes
Kybernetika, Tome 43 (2007) no. 2, pp. 115-132.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
Classification : 03E72, 68T37
Keywords: fuzzy relation; fuzzy relation properties; fuzzy relation classes; $\ast $-transitivity; transitivity; aggregation functions; relation aggregation; triangular norms 
@article{KYB_2007__43_2_a1,
     author = {Drewniak, J\'ozef and Dudziak, Urszula},
     title = {Preservation of properties of fuzzy relations during aggregation processes},
     journal = {Kybernetika},
     pages = {115--132},
     publisher = {mathdoc},
     volume = {43},
     number = {2},
     year = {2007},
     mrnumber = {2343390},
     zbl = {1135.68050},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2007__43_2_a1/}
}
TY  - JOUR
AU  - Drewniak, Józef
AU  - Dudziak, Urszula
TI  - Preservation of properties of fuzzy relations during aggregation processes
JO  - Kybernetika
PY  - 2007
SP  - 115
EP  - 132
VL  - 43
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KYB_2007__43_2_a1/
LA  - en
ID  - KYB_2007__43_2_a1
ER  - 
%0 Journal Article
%A Drewniak, Józef
%A Dudziak, Urszula
%T Preservation of properties of fuzzy relations during aggregation processes
%J Kybernetika
%D 2007
%P 115-132
%V 43
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KYB_2007__43_2_a1/
%G en
%F KYB_2007__43_2_a1
Drewniak, Józef; Dudziak, Urszula. Preservation of properties of fuzzy relations during aggregation processes. Kybernetika, Tome 43 (2007) no. 2, pp. 115-132. http://geodesic.mathdoc.fr/item/KYB_2007__43_2_a1/