$$p,q,r-$$Fractional fuzzy sets and their aggregation operators and applications
Why this work is in the frame
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Bibliographic record
Abstract
Using $$p,q,r-$$ fractional fuzzy sets ( $$p,q,r-$$ FFS) to demonstrate the stability of cryptocurrencies is considered due to the complex and volatile nature of cryptocurrency markets, where traditional models may fall short in capturing nuances and uncertainties. $$p,q,r-$$ FFS provides a flexible framework for modeling cryptocurrency stability by accommodating imprecise data, multidimensional analysis of various market factors, and adaptability to the unique characteristics of the cryptocurrency space, potentially offering a more comprehensive understanding of the factors influencing stability. Existing studies have explored Picture Fuzzy Sets and Spherical Fuzzy Sets, built on membership, neutrality, and non-membership grades. However, these sets can’t reach the maximum value (equal to $$1$$ ) due to grade constraints. For example, when considering $$\wp =(h,\langle \text{0.9,0.8,1.0}\rangle \left|h\in H\right.)$$ , these sets fall short. This is obvious when a decision-maker possesses complete confidence in an alternative, they have the option to assign a value of 1 as the assessment score for that alternative. This signifies that they harbor no doubts or uncertainties regarding the chosen option. To address this, $$p,q,r-$$ Fractional Fuzzy Sets ( $$p,q,r-$$ FFSs) are introduced, using new parameters $$p$$ , $$q$$ , and $$r$$ . These parameters abide by $$p$$ , $$q\ge 1$$ and $$r$$ as the least common multiple of $$p$$ and $$q$$ . We establish operational laws for $$p,q,r-$$ FFSs. Based on these operational laws, we proposed a series of aggregation operators (AOs) to aggregate the information in context of $$p,q,r-$$ fractional fuzzy numbers. Furthermore, we constructed a novel multi-criteria group decision-making (MCGDM) method to deal with real-world decision-making problems. A numerical example is provided to demonstrate the proposed approach.
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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 | 0.003 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it