Geodesic
Properties of fuzzy relations powers
Kybernetika, Tome 43 (2007) no. 2, pp. 133-142

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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.
Classification : 03E72, 15A33, 15A99, 16Y60
Keywords: fuzzy relation; binary operation; relation composition; $\sup \nolimits $-$\ast $ composition; relation powers; relation closure; relation interior 
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     author = {Drewniak, J\'ozef and P\c{e}kala, Barbara},
     title = {Properties of fuzzy relations powers},
     journal = {Kybernetika},
     pages = {133--142},
     publisher = {mathdoc},
     volume = {43},
     number = {2},
     year = {2007},
     mrnumber = {2343391},
     zbl = {1135.03022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2007__43_2_a2/}
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Drewniak, Józef; Pȩkala, Barbara. Properties of fuzzy relations powers. Kybernetika, Tome 43 (2007) no. 2, pp. 133-142. http://geodesic.mathdoc.fr/item/KYB_2007__43_2_a2/