Properties of fuzzy relations powers
Józef Drewniak; Barbara Pȩkala
Kybernetika (2007)
- Volume: 43, Issue: 2, page 133-142
- ISSN: 0023-5954
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topDrewniak, Józef, and Pȩkala, Barbara. "Properties of fuzzy relations powers." Kybernetika 43.2 (2007): 133-142. <http://eudml.org/doc/33847>.
@article{Drewniak2007,
abstract = {Properties of $\sup \nolimits $-$\ast $ compositions of fuzzy relations were first examined in Goguen [8] and next discussed by many authors. Power sequence of fuzzy relations was mainly considered in the case of matrices of fuzzy relation on a finite set. We consider $\sup \nolimits $-$\ast $ powers of fuzzy relations under diverse assumptions about $\ast $ operation. At first, we remind fundamental properties of $\sup \nolimits $-$\ast $ composition. Then, we introduce some manipulations on relation powers. Next, the closure and interior of fuzzy relations are examined. Finally, particular properties of fuzzy relations on a finite set are presented.},
author = {Drewniak, Józef, Pȩkala, Barbara},
journal = {Kybernetika},
keywords = {fuzzy relation; binary operation; relation composition; $\sup \nolimits $-$\ast $ composition; relation powers; relation closure; relation interior; Fuzzy coalition; Relation composition; sup-* composition; Relation powers; Relation closure, Relation interior},
language = {eng},
number = {2},
pages = {133-142},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Properties of fuzzy relations powers},
url = {http://eudml.org/doc/33847},
volume = {43},
year = {2007},
}
TY - JOUR
AU - Drewniak, Józef
AU - Pȩkala, Barbara
TI - Properties of fuzzy relations powers
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 2
SP - 133
EP - 142
AB - Properties of $\sup \nolimits $-$\ast $ compositions of fuzzy relations were first examined in Goguen [8] and next discussed by many authors. Power sequence of fuzzy relations was mainly considered in the case of matrices of fuzzy relation on a finite set. We consider $\sup \nolimits $-$\ast $ powers of fuzzy relations under diverse assumptions about $\ast $ operation. At first, we remind fundamental properties of $\sup \nolimits $-$\ast $ composition. Then, we introduce some manipulations on relation powers. Next, the closure and interior of fuzzy relations are examined. Finally, particular properties of fuzzy relations on a finite set are presented.
LA - eng
KW - fuzzy relation; binary operation; relation composition; $\sup \nolimits $-$\ast $ composition; relation powers; relation closure; relation interior; Fuzzy coalition; Relation composition; sup-* composition; Relation powers; Relation closure, Relation interior
UR - http://eudml.org/doc/33847
ER -
References
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