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CATEGORY OF (POM)L-FUZZY GRAPHS AND HYPERGRAPHS

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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 obtain some related results. In particular we construct the categories of the above mentioned notions, and give a (full and faithful) functor form the category of (POM )/,-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 also exists

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