On the $L$-valued categories of $L$-$E$-ordered sets

summary: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