Ranking fuzzy numbers by volume of solid of revolution of membership function about axis of support
Bibliographic record
Abstract
It is admissible that fuzzy numbers (FNs) are apt for representing imprecise or vague data in real-world problems. While using FNs in decision-making problems, selecting the best alternative among available alternatives is challenging, and therefore, ranking FNs is essential. We can find different studies in the literature, but to our knowledge, no one attempted to rank FNs using the concept of volume. This paper proposes a new method for ranking generalized fuzzy numbers (GFNs) using the volume of the solid obtained by revolving its membership function (MF) about the x-axis. We calculate the volumes of positive and negative sides along with the centroid of a generalized fuzzy number(GFN) to define the fuzzy number(FN) score. This score represents the defuzzified value of FN, is used to select the best alternative, and overcomes the limitations in some existing methods like ranking FNs having the same centroid, crisp numbers, symmetric fuzzy numbers, and FNs with the same core.
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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 | 0.003 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".