Fuzzy Ideals and Fuzzy Filters of Ordered Ternary Semigroups
Why this work is in the frame
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Bibliographic record
Abstract
The notion of ternary semigroups was introduced by Lehmer in 1932 and that of fuzzy sets by Zadeh in 1965. Anysemigroup can be reduced to a ternary semigroup but a ternary semigroup does not necessarily reduce to a semigroup.A partially ordered semigroup T is called an ordered ternary semigroup if for all x1; x2; x3; x4 2 T; x1 x2 impliesx1x3x4 x2x3x4; x3x1x4 x3x2x4 and x3x4x1 x3x4x2. In this paper, we study fuzzy ternary subsemigroups (left ideals,right ideals, lateral ideals, ideals) and fuzzy left filters (right filters, lateral filters, filters) of ordered ternary semigroups.
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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 | 0.027 | 0.017 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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