Hesitant Fuzzy Ordered Linguistic Term Sets for Group Decision-Making
Bibliographic record
Abstract
Characterizing uncertainty remains a critical challenge in group decision-making, which has prompted the development of diverse linguistic expressions with flexibility and applicability. However, they predominantly use adaptive linguistic terms coupled with numerical importance degrees, which inherently embed subjective cognitive biases. To address this gap, this study originally introduces hesitant fuzzy ordered linguistic term sets (HFOLTSs), which systematically address dual uncertainties: cognitive ambiguity quantified through multiple linguistic term sets, and importance indeterminacy mitigated by ordered relations. To enhance interpretability and visualization, this study proposes a graphical formalization of HFOLTSs, where hierarchical levels are embedded to reflect the structured nature of ordered relations. In addition, the fundamental operations associated with HFOLTSs, complement, expectation-based comparison, and distance measurement, are established to handle complex linguistic uncertainty. Two aggregation operators, namely, hesitant fuzzy ordered linguistic weighted averaging (HFOLWA) and hesitant fuzzy ordered linguistic ordered weighted averaging (HFOLOWA), are introduced to support group decision-making. To facilitate group consensus, we further devise a mechanism that harmoniously balances consensus efficiency with the willingness of experts. Finally, the proposed method is applied to a contractor selection problem in community renewal, which demonstrates its practicality and effectiveness in managing complex group decision scenarios.
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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 | 0.005 | 0.001 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.002 | 0.000 |
| Scholarly communication | 0.006 | 0.000 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| 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; both teacher heads agree on what is shown here.
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".