Multiary Hyperstructure and Multiary Superhyperstructure

A Hyperstructure is built on the concept of the powerset, offering a framework to model interactions among elements of a set. Extending this idea, a Superhyperstructure utilizes the n-th powerset to represent hierarchical systems with multiple layers, enabling richer abstractions and more complex relationships. In this paper, we investigate Multiary Hyperstructures and Multiary Superhyperstructures, which generalize these constructions. A multiary hyperstructure extends algebraic systems, allowing operations with multiple inputs producing set-valued outputs, thereby modeling uncertainty and multi-participant interactions. A multiary superhyperstructure further lifts multiary hyperstructures onto higher powerset levels, encoding hierarchical, layered relationships with generalized superhyper-operations across domains.