A trilevel framework of rough sets and granular rough sets: Characterizing existing models and formulating new models
Bibliographic record
Abstract
We propose a trilevel framework for studying rough sets and granular rough sets by applying the principles of three-way decision as thinking in threes. The framework builds and interprets any model of rough sets at three levels: the binary relations level concerning the relationships between objects, the granular space level concerning granules of objects, namely, sets of objects called granular objects, and the approximation level concerning the approximations of sets of objects by granular objects. We identify and characterize eight classes of rough set models, including Pawlak, covering-based, and granular rough sets. By reviewing the existing studies within the framework, we find that there is a lack of investigations on three classes. To fill in these gaps, we investigate two types of granular spaces induced by any binary relations: neighborhood-induced granular spaces and maximal-clique-induced granular spaces. We examine the properties of the two types of granular space and the properties of rough set approximations in the corresponding two classes of models. We also consider a third class of models of granular rough sets based on granular spaces without referencing a binary relation.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.003 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.006 | 0.008 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".