New Fuzzy Algebraic Structure Consists of Homomorphism via Multi-Fuzzy Set Applied to Cubic Vague Subbisemirings Over Bisemirings
Why this work is in the frame
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Bibliographic record
Abstract
We discussed that the concept of multi-fuzzy cubic vague subbisemiring (MFCVSBS) is a novel generalized hybrid structure of vague subbisemiring. The MFCVSBS and level sets using MFCVSBS of bisemirings are discussed. We define some simple operations on them, including intersection and Cartesian product, to discuss some of their basic properties under MFCVSBS. It is assumed that \(\mathcal{Z}= \langle \coprod_{i}\circ\bar{\aleph}_{\mathcal{Z}}, \coprod_{i}\circ\beth_{\mathcal{Z}} \rangle\) is the multi-fuzzy cubic vague subset of k. Assuming that any non-empty level set \(\mathcal{Z}_{(\zeta,\sigma)} (\zeta,\sigma \in D[0, 1])\) is an SBS, it can be demonstrated that \(\mathcal{Z}\) is an MFCVSBS. It will be demonstrated that MFCVSBS is both its homomorphic image and pre-image. Examples are given to illustrate our conclusions.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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