\((\in, \in \vee q_{k})\)-Intuitionistic Fuzzy Soft Boolean Near-Rings
Why this work is in the frame
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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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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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 it