Characterization of Bipolar Fuzzy SBG-Ideals in Sheffer Stroke BG-Algebras
Bibliographic record
Abstract
In this paper, we systematically develop the theory of bipolar-valued fuzzy sets in the setting of Sheffer stroke BG-algebras (SBG-algebras) by introducing and characterizing bipolar fuzzy SBG-subalgebras and SBG-ideals. Necessary and sufficient conditions for these structures are established via sss-cuts and ttt-cuts, along with explicit algorithms for their verification. We further investigate the relationship between bipolar-valued fuzzy sets and their crisp counterparts through constructive examples. It is shown that the intersection of bipolar fuzzy SBG-ideals preserves the ideal structure, and that the combination of the positive membership function with the complement of the negative membership function yields fuzzy SBG-ideals and subalgebras. These findings extend the algebraic framework of fuzzy logic and provide practical tools for modeling and analyzing bipolar uncertainty in algebraic systems.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.012 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| 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 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".