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：本研究提出并定义了自决性存在粒子这一新概念，并从代数、拓扑与部分学三个维度对其进行了刻画。存在粒子是指那些初始状态下自我决定、随后与环境产生交互的粒子。尽管该概念（如粒子球实例）在他人的早期工作中存在定义不充分、算法构建不规范及理论化不足等问题，但已在粗糙集与软计算应用中得到实际运用。研究表明，这些概念能够适配粒计算的多种理论框架（包括公理化框架与自适应框架等）。此项刻画旨在推动算法开发、分类问题应用，并为该方法推广提供可能的数学基础。此外，本文还提出了多个有待解决的开放性问题，并指明了未来研究方向。