Category of (POM)_L-Fuzzy Graphs and Hypergraphs

In this note by considering a complete lattice L, we define the notion of an L-Fuzzy hyperrelation on a given non-empty set X. Then we define the concepts of (POM)_L-Fuzzy graph, hypergraph and subhypergroup and then obtain some related results. In particular we construct the categories of the above mentioned notions, and then give a (full and faithful) functor form the category of (POM)_L-Fuzzy subhypergroups ((POM)_L-Fuzzy graphs) into the category of (POM)_L-Fuzzy hypergraphs. Also we show that for each finite objects in the category of (POM)_L-Fuzzy graphs, the coproduct exists, and under a suitable condition the product exists too.