Verifying and managing additive consistency and deriving weights for hesitant fuzzy preference relations
Bibliographic record
Abstract
Hesitant fuzzy preference relation (HFPR) is a valid tool to describe the hesitation, ambiguity and uncertainty of decision makers. As a crucial criterion to ensure the rationality of preferences and final decision results, the consistency of preference relations is a valuable research topic. In this study, the additive consistency of HFPRs is investigated. Two kinds of consistency, completely additive and weakly additive, for HFPRs are introduced. Some 0–1 mixed programming models and simple algebraic operations are developed to detect the additive consistency type for HFPRs. Further, the priority weights of a consistent HFPR can be derived by constructing and solving two linear programming models. If an HFPR is identified to be inconsistent, we present a straightforward method to rectify inconsistency. Then, an integrated algorithm is proposed to ascertain the additive consistency type, improve consistency and rank alternatives. Finally, the applicability and validity of this proposal are verified through a case study, discussion and comparative analysis with the existing methods.
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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 | 0.016 | 0.044 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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".