On Consistency in AHP and Fuzzy AHP
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract The analytic hierarchy process (AHP) is used widely for analyzing decisions made in various real-world applications. Its basic idea is to construct a hierarchy of concepts encountered in a given decision problem and to choose the best alternative according to pairwise comparison matrices given by the decision maker. Under the assumption of fully rational economics, a reasonable decision should be consistent. It becomes an important issue on how to analyze and ensure the consistency of comparison matrices together with the judgments of the decision maker. The main objectives of the present paper are threefold. First, we review the basic idea and methods used to define the consistency and the transitivity of multiplicative reciprocal matrices, additive reciprocal matrices and comparison matrices with fuzzy interval and triangular fuzzy numbers. The existing controversy behind the applications of fuzzy set theory to the AHP in the literature is presented. Second, the consistency of the collective comparison matrices in group decision making based on AHP and fuzzy AHP is further analyzed. We point out that the weak consistency of preference relations with fuzzy numbers in fuzzy AHP and group decision making should be investigated comprehensively. Third, under the consideration of the vagueness in the process of evaluating the judgements, a new concept of fuzzy consistency of comparison matrices in the AHP is given.
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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 | 0.004 | 0.016 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.002 |
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