\((\in, \in \vee q_{k})\)-Intuitionistic Fuzzy Soft Boolean Near-Rings
Bibliographic record
Abstract
This study proposes an enriched algebraic framework through the introduction of (∈, ∈ ∨qk)-intuitionistic fuzzy soft Boolean near-rings (IFSBNs), a class of mathematical structures that generalize previous fuzzy and soft ideal systems within Boolean near-rings. Building upon established theories, we define the corresponding (∈, ∈ ∨qk)- intuitionistic fuzzy soft ideals (IFSIs) and idealistic forms (IIFSBNs), and rigorously analyze their properties using formal definitions and examples. By expanding the capacity to model uncertainty and complex relationships, this work contributes to the theoretical backbone required for developing future intelligent systems. Importantly, the abstract nature of these algebraic tools makes them highly adaptable to curriculum designs in mathematics-focused educational environments, aligning with Sustainable Development Goal 4 (Quality Education). In particular, the framework can inspire high school and university students in research-intensive programs to engage in exploratory learning and abstract reasoning. Furthermore, this contribution exemplifies how collaborative academic efforts across institutions can produce foundational knowledge that transcends disciplinary boundaries, supporting SDG 17 (Partnerships for the Goals). The cross-institutional authorship and integration of interdisciplinary concepts promote educational equity and intellectual cooperation, fostering a culture of shared research innovation globally.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
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".