In this chapter, we present fundamental and technical concepts like fuzzy hypergraphs, fuzzy column hypergraphs, fuzzy row hypergraphs, fuzzy competition hypergraphs, fuzzy k-competition hypergraphs, fuzzy neighborhood hypergraphs, and N -hypergraphs. We describe applications of fuzzy competition hypergraphs in decision support systems, including predator-prey relations in ecological niches, social networks, and business marketing. Further, we introduce complex fuzzy hypergraphs, μe iθ −level hypergraphs, covering constructions, 2-sections, and L 2 -sections of these hypergraphs. We define certain new products, including Cartesian product, minimal rank preserving, and maximal rank preserving direct products on complex fuzzy hypergraphs. Moreover, we present an application of our proposed model to illustrate the publication data in co-authorship networks. This chapter is basically due to [3, 7-9, 12, 25].