A Consistency and Consensus-Based Goal Programming Method for Group Decision-Making With Interval-Valued Intuitionistic Multiplicative Preference Relations
Bibliographic record
Abstract
Interval-valued intuitionistic multiplicative preference relations (IVIMPRs) form a suitable conceptual framework to represent and process simultaneously uncertain preferred and nonpreferred judgments of decision makers (DMs). The focus of this paper is on group decision-making (GDM) problems realized with IVIMPRs. First, a consistency index is introduced to evaluate the consistency degree for intuitionistic multiplicative preference relations (IMPRs), and a consistency optimization approach is presented to jointly improve the consistency degrees of several IMPRs that do not satisfy the predefined consistency threshold. Then, a consistency definition and an acceptable consistency definition for IVIMPRs are established by splitting an IVIMPR into two IMPRs. For several IVIMPRs with unacceptable consistency, a goal program-based approach is proposed to simultaneously improve their consistency. Subsequently, by minimizing the degree to which the opinions of individual DMs deviate from those of the group, a maximum consensus-based goal program is established to determine the DMs' weights. Furthermore, an aggregation approach is applied to integrate individual IVIMPRs into a collective one. A linear program is then built to determine the interval-valued intuitionistic multiplicative priority weights of alternatives coming from the collective IVIMPR. A consistency-based GDM algorithm is proposed. Finally, a practical example is offered to show the application of the new algorithm, and a comparative analysis is presented to highlight the advantages of the new method.
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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 | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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; a candidate call from one teacher head, 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".