Examples of Topological Modeling of Matrix-Structured Data and Use of the Applied Attachment Function of the Cellular Data System

In the era of "Big Data", a large amount of unstructured and diverse data is being stored, and data and its dependencies between systems or functions progress and change constantly, as users\´ requirements change. Such information worlds are called cyber worlds. We need a more powerful mathematical background which can model the cyber worlds as they are. We consider the Incrementally Modular Abstraction Hierarchy (IMAH) to be most appropriate for modeling the dynamically changing cyber worlds by descending from the most abstract homotopy level to the most specific view level, while preserving invariants. In our research, we have developed a data processing system called the Cellular Data System (CDS) based on IMAH. In this paper, firstly we introduce an aggregation function, positioned as an applied function of the attachment function. Secondly, we deal with matrix-structured data for parts information management by CDS, solving the difficulty arising from the complexity of information about parts and combinations of parts.