Fuzzy Generalized Fractal Dimensions on Sierpiński and Social Network Graphs
Bibliographic record
Abstract
Fractal theory is the propelled technique to analyze non-linear systems and complex graphs. The quantification of complexity in Sierpiński and social network graphs requires the estimation of Generalized Fractal Dimensions (GFD), where complexity refers to the greater inconsistency and uncertain nature of the systems. This study introduces the fuzzy version of GFD and compares the Fuzzy GFD (FGFD) with the usual GFD for extended Sierpiński and social network graphs. The computational results indicate that the complexity of the graphical structure increases with the number of iterations due to self-similarity, as fractal-based measure values increase with iterations for generalized Sierpiński graphs. The FGFD values are consistently higher than the usual GFD, demonstrating its ability to capture more structural information. Thus, FGFD provides a more effective method for estimating non-linearity and analyzing Sierpiński and real-time graphical networks. The proposed fuzzy-based multifractal measures better quantify complexity levels compared to traditional multifractal measures.
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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 | 0.000 | 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 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".