Exploring Multipolar Fuzzy Hyperfilters in Ordered Semihypergroups
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Bibliographic record
Abstract
The notion of multipolar fuzzy sets ([Formula: see text]-p[Formula: see text]s) extends the idea of bipolar fuzzy sets and offers a powerful framework for dealing with multiattribute data under uncertainty. While several research papers have been published on fuzzy hyperfilters and bipolar fuzzy hyperfilters in ordered semihypergroups, the study of hyperfilters within the multipolar fuzzy setting has remained unexplored. In this work, we advance the theoretical foundation of hyperfilters in ordered semihypergroups by applying [Formula: see text]-p[Formula: see text]s. Specifically, we introduce the concepts of [Formula: see text]-[Formula: see text] left and right hyperfilters, and examine their essential properties through multipolar level sets and multipolar characteristic fuzzy sets. We show that arbitrary intersection of [Formula: see text]-[Formula: see text] left/right hyperfilters is an [Formula: see text]-[Formula: see text] left/right hyperfilter, whereas arbitrary union of [Formula: see text]-[Formula: see text] left/right hyperfilters is not necessarily an [Formula: see text]-[Formula: see text] left/right hyperfilter which is shown by an illustrative example. We provide a sufficient condition under which union of [Formula: see text]-[Formula: see text] left/right hyperfilters is an [Formula: see text]-[Formula: see text] left/right hyperfilter. Furthermore, we define and investigate [Formula: see text]-[Formula: see text] bi-hyperfilters, and explore their relationships with [Formula: see text]-p completely prime fuzzy hyperideals and [Formula: see text]-p completely prime fuzzy bi-hyperideals.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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