New Fuzzy Algebraic Structure Consists of Homomorphism via Multi-Fuzzy Set Applied to Cubic Vague Subbisemirings Over Bisemirings
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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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".