A Spanning Tree-Induced Method to Derive Weights From Fuzzy Preference Relations: A Monte Carlo Simulation-Based Investigation
Bibliographic record
Abstract
Deriving the priority weights from fuzzy preference relations (FPRs) forms an interesting, promising, and practically oriented research topic. Using the spanning tree tool present in graph theory, we develop a spanning tree-induced method (SPIM) to induce the weight vectors from preference information. The essence of this method is to extract all possible “key combinations” from an FPR and then compute all possible weight vectors. The arithmetic mean (AM) and geometric mean (GM) of these weight vectors are the overall weight vectors of the FPR. Based on the accumulation of squared deviations between the overall weight vector and all possible weight vectors, we define a new measure of inconsistency. The SPIM exhibits three essential characteristics; this method not only produces all possible weight vectors but also identifies their sources. Consequently, this approach can further facilitate the inconsistency analysis, and this method can be directly applied to incomplete FPRs without estimating missing elements. Additionally, we prove the mathematical equivalence of the GM of weight vectors derived from all spanning trees to that of the logarithmic least-squares method (LLSM). Without loss of generality, we adopt the Monte Carlo simulations and report a comparison analysis to provide strong evidence for the advantages and effectiveness of our proposed method.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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 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".