Hierarchy grey relational analysis using DEA and AHP
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Bibliographic record
Abstract
Purpose This paper aims to apply an integrated data envelopment analysis (DEA) and analytic hierarchy process (AHP) approach to a multi-hierarchy grey relational analysis (GRA) model. Consistent with the most real-life applications, the authors focus on a two-level hierarchy in which the attributes of similar characteristics can be grouped into categories. Nevertheless, the proposed approach can be easily extended to a three-level hierarchy in which attributes might also belong to different sub-categories and further be linked to categories. Design/methodology/approach The procedure of incorporating the DEA and AHP methods in a two-level GRA may be broken down into a series of steps. The first three steps are under the heading of attributes and the latter three steps are under the heading of categories as follows: computing the grey relational coefficients of attributes for each alternative using the basic GRA model which further provides the required (output) data for an additive DEA model; computing the priority weights of attributes and categories using the AHP method which provides a priori information on the adjustments of attributes and categories in additive DEA models; computing the grey relational grades of attributes in each category for alternatives using an additive DEA model; converting the grey relational grades of attributes to the grey relational coefficients of categories; computing the grey relational grades of categories for alternatives using an additive DEA model; computing the dissimilarity grades of categories for the tied alternatives using an additive DEA exclusion model. Findings The proposed approach provides a more reasonable and encompassing measure of performance in a hierarchy GRA, based on which the overall ranking position of alternatives is obtained. A case study of a wastewater treatment technology selection verifies the effectiveness of this approach. Originality/value This research is a step forward to overcome the current shortcomings in a hierarchy GRA by extracting the benefits from both the objective and subjective weighting 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 | 0.035 | 0.046 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
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