Bibliographic record
Abstract
A rough set theory (RST) was developed by Zdzislaw Pawlak to handle vagueness and uncertainty in data analysis.An approximation of a vague concept consists of two precise concepts a lower and an upper approximation.These approximations are two basic operations in rough set theory.An upper approximation contains all objects that may possibly belong to a concept, and a lower approximation contains all objects that certainly belong.The boundary region is the difference between the upper and lower approximations.Thus, rough set theory expresses vagueness by using a boundary region of a set rather than by using membership.By using the pair of sets, rough set theory extends traditional set theory by defining a subset of a universe.The properties of any set can be clearly understood if an algebraic structure is developed.This paper considers an approximation space with a finite universe and introduces a rough action by a symmetric group S|U| acting on all rough sets in this space.Also, we proved that the number of orbits of the symmetric group S|U| in rough sets is one.We then introduced the S|U|-submodule and proved that the kernel of rough homomorphism is a rough || submodule.An example of how rough action can be used to find missing values in sample cancer data has also been provided.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".