Up-directed rough sets are introduced and studied by the present author in earlier papers. This is extended by her in two different granular directions in this research, with a surprising algebraic semantics. The granules are based on ideas of generalized closure under up-directedness that may be read as a form of weak consequence. This yields approximation operators that satisfy cautious monotony, while pi-groupoidal approximations (that additionally involve strategic choice and algebraic operators) have nicer properties. The study is primarily motivated by possible structure of concepts in distributed cognition perspectives, real or virtual classroom learning contexts, and student-centric teaching. Rough clustering techniques for datasets that involve up-directed relations (as in the study of Sentinel project image data) are additionally proposed. This research is expected to see significant theoretical and practical applications in related domains.
翻译:本文作者在先前的论文中介绍并研究了上向型粗金刚石组。 本文作者在先前的论文中介绍了这些粗金刚石组,在这项研究的两个不同的颗粒方向上扩展了这一项研究,其中的代数语义语义语系令人惊讶。 这些颗粒基于在上向型下普遍封闭的想法,这些想法可能被视为一种微弱的后果。这产生了满足谨慎单调的近似操作者,而小类近似(另外涉及战略选择和代数操作者)则具有较好的特性。 这项研究主要受分布式认知视角、实际或虚拟课堂学习环境以及以学生为中心的教学中可能存在的概念结构的驱动。 还提出了涉及上向型关系的数据集组合技术(如Sentinel项目图像数据的研究中),预计这项研究将在相关领域看到重要的理论和实践应用。