$$p,q,r-$$Fractional fuzzy sets and their aggregation operators and applications
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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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".