An Asymmetric Approach to Three-Way Approximation of Fuzzy Sets
Bibliographic record
Abstract
The three-way approximation of fuzzy sets represents membership values using a three-valued set$\lbrace \mathbf{1}, \mathbf{m}, \mathbf{0}\rbrace$, where1indicates total belongingness,0total non-belongingness, andman intermediate state. This approach elevates values of membership function above a threshold$\alpha$to1, reduces those below$\beta$to0, and assigns the remaining ones to an intermediate valuem. A key challenge lies in determining the thresholds$\alpha$and$\beta$and selecting the value ofm, as existing models often lack analytical solutions and fail to fully explore the relationship betweenmand membership structures. This study introduces an asymmetric three-way approximation model for fuzzy sets, removing the constraint$\alpha + \beta = 1$. An analytical formula is derived for the thresholds$(\alpha, \beta)$by minimizing information loss, and the relationship betweenmand membership structures is thoroughly examined. An adaptive optimizer is proposed to learn the approximate optimal value ofmby minimizing the information loss. The experimental results show that information loss decreases initially before increasing asmgrows. Besides, our model achieves the best classification across most datasets.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".