Employing the Bellman-Ford Algorithm with Score Functions to Address the Linear Diophantine Fuzzy Shortest Path Problem in Network Analysis
Bibliographic record
Abstract
The realms of Intuitionistic Fuzzy Sets (IFSs), Pythagorean Fuzzy Sets (PFS), and qrung Orthopair Fuzzy Sets (q-ROFSs) have found extensive applications across various disciplines, notably in resolving real-world problems.However, limitations concerning membership and non-membership grades pose challenges to these theories.Efforts to mitigate these constraints have led to the introduction of a new concept, the Linear Diophantine Fuzzy Set (LDFS), with reference parameters.This study advances the shortest path (SP) problem for Linear Diophantine Fuzzy graphs.An innovative method for constructing direct network graphs within a Linear Diophantine Fuzzy (LDF) context is proposed.Distances or costs between nodes are encapsulated by Linear Diophantine Fuzzy numbers.The principal contribution of this investigation lies in proposing a novel approach to solving the Linear Fuzzy Diophantine Fuzzy shortest path problem using the Bellman-Ford algorithm for optimal solution attainment.Usage of the score function enables the comparison and identification of the minimum arc value between nodes.The proposed algorithm's validity is demonstrated through a numerical example, and a comparison with existing methodologies underscores the benefits of the proposed 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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 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".