A Comparative Study Between Analytic Hierarchy Process and Its Fuzzy Variants: A Perspective Based on Two Linguistic Models
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Bibliographic record
Abstract
The analytic hierarchy process (AHP) is widely employed to guide the decision-maker to rank or evaluate the alternatives in decision activities. Its fuzzy set-based version, i.e., the fuzzy AHP, has also been widely studied and applied since its inception. The essential distinction between the AHP and fuzzy AHP comes from the diverse transformation methods between the linguistic and numeric judgments. In this article, we conduct a thorough comparative study between the AHP and fuzzy AHP methods in the framework of two linguistic models, i.e., the linguistic model based on the membership functions and two-tuple linguistic model. First, four AHP and three fuzzy AHP methods are revisited with the involvement of two linguistic models. Then, the comparison criteria are involved by calculating the cardinal or ordinal deviation between the original information and decision solutions, and the effects of the transitivity of the reciprocal matrix are also discussed in the comparative study. Finally, the detailed experiments along with a thorough comparative analysis are conducted based on the random and publicly available data to show the difference between the AHP and fuzzy AHP methods.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 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 it