Introduction to Preference Modeling with Binary Fuzzy Relations
Bibliographic record
Abstract
This chapter presents an introduction to preference modeling realized in terms of binary fuzzy relations and address certain difficulties that arise in the extension of the classical or Boolean preference structures of binary relations to the fuzzy environment. Particularly, the extension of the classical structures to their fuzzy counterparts requires the selection of a De Morgan triplet and of adequate functions to construct suitable binary fuzzy relations of strict preference, indifference, and incomparability. Unfortunately, it is not that simple to implement this extension. In this context, the current chapter recalls some concepts related to binary fuzzy relations and some specific t-norms, t-conorms, and negation operators, which will play an important role. The chapter defines preference structures of binary fuzzy relations and outlines a method for constructing these fuzzy structures, without losing important characteristics of the classical preference structures of binary relations. Controlled Vocabulary Terms fuzzy set theory; model reference adaptive control systems
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.047 | 0.010 |
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".