A hypergraph is one of the most developing area for modeling various practical problems in different fields, including computer science, biological sciences, social networks and psychology. Our main discussion in this research paper is to apply the notion of intuitionistic fuzzy sets to extend the theory of hypergraphs. We introduce the concept of isomorphism, dual intuitionistic fuzzy hypergraph, intuitionistic fuzzy line graph and 2-section of an intuitionistic fuzzy hypergraph. We present some applications of intuitionistic fuzzy hypergraphs in planet surface networks, selection of authors of of intersecting communities in a social network and grouping of incompatible chemical substances. We design certain algorithms to construct dual intuitionistic fuzzy hypergraph, intuitionistic fuzzy line graph and the selection of objects in decision-making problems.
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