Olga Grigorenko

# Abstract:

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.

# Keywords:

category, $L$-valued category, fuzzy order relation

# Classification:

03E72, 18A05, 18B35

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