Hyperfilters and Convex Subhyperlattices in a Join Hyperlattice

In this paper, we define different types of hyperfilters in a join hyperlattice. We prove that these types of hyperfilters are equivalent in a join P-hyperlattice whereas, only type-II and type-III hyperfilters are equivalent in a Nakano hyperlattice. We define the notion of convex subhyperlattice in a join hyperlattice and discuss various properties with suitable examples. Finally, we prove that any convex subhyperlattice in a P-hyperlattice or Nakano hyperlattice can be uniquely represented as the intersection of a hyperideal and a hyperfilter, and illustrate with suitable examples.