Optimal approximation of nonlinear functions by fuzzy systems
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Bibliographic record
Abstract
This paper presents a novel approach to the optimal approximation of nonlinear functions employing fuzzy systems. The proposed approach, which is based on a genetic algorithm, also illustrates the underlying design principles of different parts of a fuzzy system. This insight is facilitated by our definition of characteristic points. To appreciate this concept, an illustrative example is employed. The essence of this paper is the fact that the conventional selection of membership functions does not lead to the best function approximation. It is also demonstrated that while a fuzzy system with triangular membership functions is, in effect, a linear piecewise approximation of a nonlinear function, a fuzzy system with gaussian member functions can be viewed as a nonlinear piecewise approximation of the same nonlinear function.
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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 | 0.000 | 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 | 0.000 | 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