On Hesitant Fuzzy Subalgebraic Systems in IUP-Algebras
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Bibliographic record
Abstract
We introduce hesitant fuzzy sets of algebraic structures in IUP-algebras, including hesitant fuzzy IUP-subalgebras, IUP-filters, IUP-ideals, and strong IUP-ideals. These notions are defined via relaxed set-theoretic and algebraic conditions suitable for hesitant fuzzy membership functions. Their mutual relationships are analyzed, showing how they extend and unify prior definitions in the UP-algebraic setting. Several examples and counterexamples are provided to illustrate essential differences between these classes and to demonstrate that each concept is a proper generalization of its classical or fuzzy counterpart. A diagram of class inclusions is also presented to visualize the structural hierarchy among these hesitant fuzzy sets.
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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 | 0.004 | 0.001 |
| 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 | 0.001 | 0.000 |
| Open science | 0.002 | 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