Geodesic
On the $L$-valued categories of $L$-$E$-ordered sets
Kybernetika, Tome 48 (2012) no. 1, pp. 144-164

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The aim of this paper is to construct an $L$-valued category whose objects are $L$-$E$-ordered sets. To reach the goal, first, we construct a category whose objects are $L$-$E$-ordered sets and morphisms are order-preserving mappings (in a fuzzy sense). For the morphisms of the category we define the degree to which each morphism is an order-preserving mapping and as a result we obtain an $L$-valued category. Further we investigate the properties of this category, namely, we observe some special objects, special morphisms and special constructions.
Classification : 03E72, 18A05, 18B35
Keywords: category; $L$-valued category; fuzzy order relation 
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     author = {Grigorenko, Olga},
     title = {On the $L$-valued categories of $L$-$E$-ordered sets},
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     pages = {144--164},
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     volume = {48},
     number = {1},
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     zbl = {1251.03062},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012__48_1_a8/}
}
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Grigorenko, Olga. On the $L$-valued categories of $L$-$E$-ordered sets. Kybernetika, Tome 48 (2012) no. 1, pp. 144-164. http://geodesic.mathdoc.fr/item/KYB_2012__48_1_a8/