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.

翻译：本研究提出了能够自我确定的存在性粒子的新概念，并从代数、拓扑和分体论视角对其进行了刻画。存在性粒子是指那些最初自我确定、随后与所处环境相互作用的粒子。尽管早期文献中对这类概念（如粒度球）的定义不够充分、算法构建欠完善且理论基础薄弱，但此类概念已应用于粗糙集与软计算领域。研究表明，这些概念符合粒计算的多种理论框架（包括公理化框架与自适应框架等）。该刻画旨在为算法开发、分类问题应用以及方法泛化的可能数学基础提供支撑。此外，本文提出了多项开放性问题和未来研究方向。