# Algebraic, Topological, and Mereological Foundations of Existential Granules

arXiv: https://arxiv.org/abs/2308.16157 · HTML: https://mlsanity.com/paper/2308.16157/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 35 references that are in the map.
- First posted on arXiv 30 Aug 2023.

## Builds on (most cited first, 2 of 2)

- [An Efficient and Adaptive Granular-ball Generation Method in Classification Problem](https://mlsanity.com/paper/2201.04343/) (2022)
- [Rough Randomness and its Application](https://mlsanity.com/paper/2304.00005/) (2023)

## Abstract (arXiv)

In this research, new concepts of existential granules that determine themselves are invented, and are characterized from algebraic, topological, and mereological perspectives. Existential granules are those that determine themselves initially, and interact with their environment subsequently. Examples of the concept, such as those of granular balls, though inadequately defined, algorithmically established, and insufficiently theorized in earlier works by others, are already used in applications of rough sets and soft computing. It is shown that they fit into multiple theoretical frameworks (axiomatic, adaptive, and others) of granular computing. The characterization is intended for algorithm development, application to classification problems and possible mathematical foundations of generalizations of the approach. Additionally, many open problems are posed and directions provided.