Abstract
A graph in which the edge can connect more than two vertices is called a Hypergraph. A ''k''-partite hypergraph is a hypergraph whose vertices can be split into ''k'' different independent sets. In this paper, regular, totally regular, totally irregular, totally neighborly irregular Intuitionistic Fuzzy ''k''-Partite Hypergraphs (IF''k''-PHGs) are defined. Also order and size along with the properties of regular and totally regular IF''k''-PHGs are discussed. It has been proved that the size <math>S(\mathscr{H})</math> of a ''r''-regular IF''k''-PHG is <math>\frac{tr}{2}</math> where <math>t=\left|V\right|</math>. The dual IF''k''-PHG has also been defined with example.
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