Study on multidimensional fuzzy graphs through modified partial ordering
Bibliographic record
Abstract
This paper introduces the concepts of multidimensional fuzzy graphs and edge-powered multidimensional fuzzy graphs, which employ a hybrid structure that combines multidimensional fuzzy sets and graphs. This study redefines the axioms of multidimensional $t-$ norms and $t-$ conorms by providing a more general partial order that can link more components of the range set $\mathcal{J}_{\infty}\big([0,1]\big)$. More studies on various operations such as direct product, composition, tensor product, join, etc. are conducted with relevant illustrations. A novel complement operator approach is also investigated to link the multidimensional fuzzy graph and the edge-powered multidimensional fuzzy graph. Finally, defining the infimum and supremum of an arbitrary family in $\mathcal{J _{\infty}\big([0,1]\big)$ introduces many notions such as vertex degree, $min-$ vertex degree, $max-$ vertex degree, path strength, etc.
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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 | 0.004 | 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 | 0.001 | 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 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".