Supermodular HyperFunctions and Monotone HyperFunctions

A hyperfunction associates each input with a set of admissible outputs, extending ordinary functions by permitting multivalued images rather than single values. A superhyperfunction uses iterated powersets for its domain and codomain, so it can encode hierarchical, multi-level output structure and hyperstructural multivalued behavior across a system. In this paper, we investigate supermodular hyperfunctions and monotone hyperfunctions, focusing on how these properties interact with such hierarchical, set-valued mappings.