Selected Concepts of MetaStructure: Cube, HyperCube, Matrix, Decision-Making, Neural Networks, Geometry, and Functions

Abstract

A MetaStructure is a higher-level framework that regards collections of structures as single objects, endowed with natural operations that preserve isomorphisms across domains. An Iterated MetaStructure extends this idea recursively, producing successive layers in which structures of structures give rise to deeper hierarchical metalevels. In this work, we develop extensions of concepts such as Cube, HyperCube, Matrix, Decision-Making, Neural Networks, Geometry, and Functions within the settings of MetaStructure and Iterated MetaStructure. We further illustrate these extensions through simple yet concrete examples, highlighting both their mathematical generality and intuitive applicability.