Development of Granular Fuzzy Relation Equations Based on a Subset of Data
Bibliographic record
Abstract
Developing and optimizing fuzzy relation equations are of great relevance in system modeling, which involves analysis of numerous fuzzy rules. As each rule varies with respect to its level of influence, it is advocated that the performance of a fuzzy relation equation is strongly related to a subset of fuzzy rules obtained by removing those without significant relevance. In this study, we establish a novel framework of developing granular fuzzy relation equations that concerns the determination of an optimal subset of fuzzy rules. The subset of rules is selected by maximizing their performance of the obtained solutions. The originality of this study is conducted in the following ways. Starting with developing granular fuzzy relation equations, an interval-valued fuzzy relation is determined based on the selected subset of fuzzy rules (the subset of rules is transformed to interval-valued fuzzy sets and subsequently the interval-valued fuzzy sets are utilized to form interval-valued fuzzy relations), which can be used to represent the fuzzy relation of the entire rule base with high performance and efficiency. Then, the particle swarm optimization (PSO) is implemented to solve a multi-objective optimization problem, in which not only an optimal subset of rules is selected but also a parameter ε for specifying a level of information granularity is determined. A series of experimental studies are performed to verify the feasibility of this framework and quantify its performance. A visible improvement of particle swarm optimization (about 78.56% of the encoding mechanism of particle swarm optimization, or 90.42% of particle swarm optimization with an exploration operator) is gained over the method conducted without using the particle swarm optimization algorithm.
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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 | 0.003 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".