Bipolar Fuzzy Quasi-Ideals in Γ-Semirings: A Study
Why this work is in the frame
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Bibliographic record
Abstract
This paper investigates bipolar fuzzy quasi-ideals in the context of Γ-semirings, offering new insights into their structural properties. Our results reveal that bipolar fuzzy quasi-ideals serve as a generalization of bipolar fuzzy ideals, while bipolar fuzzy bi-ideals extend this framework further. We also establish that in regular Γ-semirings, the two concepts coincide, leading to a unified interpretation. Notably, the intersection of a bipolar fuzzy right ideal and a bipolar fuzzy left ideal forms a bipolar fuzzy quasi-ideal, highlighting key properties that deepen our understanding of ideal structures in Γ-semirings.
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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 | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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 it