Granular Directed Rough Sets, Concept Organization and Soft Clustering
This work addresses concept organization and soft clustering in domains like distributed cognition and education, but it appears incremental as it builds on the author's prior research.
The paper extends up-directed rough sets in two granular directions, revealing a surprising algebraic semantics and proposing rough clustering techniques for datasets with up-directed relations, such as in Sentinel project image data.
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.