Optimal Solution for Fully Spherical Fuzzy Linear Programming Problem
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Bibliographic record
Abstract
This study presents an innovative extension to existing fuzzy set models, introducing the concept of spherical fuzzy sets.Distinguished by their three function characteristics-positive, neutral, and negative membership degrees-the sum of their squares is constrained to be no more than one.This paper discusses the application of these sets through the lens of fully fuzzy spherical linear programming problems, where spherical fuzzy numbers are utilized as parameters.A crisp version of the Spherical Fuzzy Linear Programming Problem (SFLPP) is generated by leveraging these membership degrees.A novel method is proposed for the de-fuzzification of spherical fuzzy numbers into crisp interval numbers.Further, the Best Worst Method (BWM) is employed to solve the crisp Linear Programming Problem (LPP).Alongside this, we propose a spherical fuzzy optimization model to resolve the SFLPP.The validity and optimality of our proposed methodology are substantiated with a detailed numerical example.
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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 | 0.000 | 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 it