On Pythagorean and Complex Fuzzy Set Operations
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Bibliographic record
Abstract
Complex fuzzy logic is a new multivalued logic system that has emerged in the last decade. At this time, there are a limited number of known instances of complex fuzzy logic, and only a partial exploration of their properties. There has also been relatively little progress in developing interpretations of complex-valued membership grades. In this paper, we address both problems by examining the recently developed Pythagorean fuzzy sets (a generalization of intuitionistic fuzzy sets). We first characterize two lattices that have been suggested for Pythagorean fuzzy sets and then extend these results to the unit disc of the complex plane. We thereby identify two new complete, distributive lattices over the unit disc, and explore interpretations of them based on fuzzy antonyms and negations.
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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 | 0.003 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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