Solving the First Kind Fuzzy Integral Equations Using a Hybrid Regularization Method and Bernstein Polynomials
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Bibliographic record
Abstract
A hybrid of regularization methodand Bernstein polynomials is used to solve the first kind fuzzy integral equations. In this paper, first the regularization method applied to convert the first kind fuzzy integral equation into the second kind fuzzy integral equation. Then by approximating Bernstein polynomials, the obtained second kind fuzzy integral equation is solved. In this method, one parameter was created in the second kind equation. When this parameter tends to zero, the solutions of integral equation of the second kind tend to solutions of the integral equation of the first kind. The obtained solutions are comparable to the solutions of the other similar methods. Performance of the mentioned method is illustrated by considering some example.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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 it