Directed Fuzzy Edge Graphs Under q-ROF Environment: A Framework for Optimal Pathfinding

This paper introduces a novel framework of Directed Edge q-Rung Orthopair Fuzzy Graphs (DEq-ROFGs), where graph vertices are crisp, and edges are characterized by q-rung orthopair fuzzy numbers (q-ROFNs). This structure captures the uncertainty in edge relationships while retaining deterministic nod...

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Main Authors: Nazia Nazir, Tanzeela Shaheen, Wajid Ali, Md Rafiul Hassan, Mohammad Mehedi Hassan
Format: Article
Language:English
Published: IEEE 2025-01-01
Series:IEEE Access
Subjects:
Online Access:https://ieeexplore.ieee.org/document/10979912/
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author Nazia Nazir
Tanzeela Shaheen
Wajid Ali
Md Rafiul Hassan
Mohammad Mehedi Hassan
author_facet Nazia Nazir
Tanzeela Shaheen
Wajid Ali
Md Rafiul Hassan
Mohammad Mehedi Hassan
author_sort Nazia Nazir
collection DOAJ
description This paper introduces a novel framework of Directed Edge q-Rung Orthopair Fuzzy Graphs (DEq-ROFGs), where graph vertices are crisp, and edges are characterized by q-rung orthopair fuzzy numbers (q-ROFNs). This structure captures the uncertainty in edge relationships while retaining deterministic node identities, making it ideal for applications in uncertain environments such as social networks, supply chains, healthcare systems, and recommendation systems. The paper defines foundational properties of DEq-ROFGs including subgraphs, completeness, and various degree-based metrics, and it establishes a proposition regarding the balance between in-degrees and out-degrees. The core contribution is a novel path-finding algorithm based on Hamacher operators and an improved score function, which identifies optimal paths between nodes under uncertainty. Unlike classical algorithms, it considers the suitability of a path, not just its length. Applied to an emergency road network scenario, the algorithm successfully determines the optimal route for service vehicles, and the choice between these routes can be made based on the score of the resulting path length. Comparative simulations show their effectiveness over traditional methods. Further analysis shows that increasing the q-value reduces both path score and length, and that Einstein operators yield higher destination scores than Hamacher and Dombi, confirming the model’s adaptability and robustness.
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issn 2169-3536
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publishDate 2025-01-01
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spelling doaj-art-ffecc02a98014a0bb986ae9ef6e2473a2025-08-20T03:49:40ZengIEEEIEEE Access2169-35362025-01-0113818238183410.1109/ACCESS.2025.356563310979912Directed Fuzzy Edge Graphs Under q-ROF Environment: A Framework for Optimal PathfindingNazia Nazir0Tanzeela Shaheen1Wajid Ali2https://orcid.org/0000-0002-4926-722XMd Rafiul Hassan3https://orcid.org/0000-0001-6381-3816Mohammad Mehedi Hassan4https://orcid.org/0000-0002-3479-3606Department of Mathematics, Air University Islamabad, Islamabad, PakistanDepartment of Mathematics, Air University Islamabad, Islamabad, PakistanDepartment of Mathematics, Air University Islamabad, Islamabad, PakistanDepartment of Computer Science, Central Connecticut State University, New Britain, CT, USAInformation Systems Department, College of Computer and Information Sciences, King Saud University, Riyadh, Saudi ArabiaThis paper introduces a novel framework of Directed Edge q-Rung Orthopair Fuzzy Graphs (DEq-ROFGs), where graph vertices are crisp, and edges are characterized by q-rung orthopair fuzzy numbers (q-ROFNs). This structure captures the uncertainty in edge relationships while retaining deterministic node identities, making it ideal for applications in uncertain environments such as social networks, supply chains, healthcare systems, and recommendation systems. The paper defines foundational properties of DEq-ROFGs including subgraphs, completeness, and various degree-based metrics, and it establishes a proposition regarding the balance between in-degrees and out-degrees. The core contribution is a novel path-finding algorithm based on Hamacher operators and an improved score function, which identifies optimal paths between nodes under uncertainty. Unlike classical algorithms, it considers the suitability of a path, not just its length. Applied to an emergency road network scenario, the algorithm successfully determines the optimal route for service vehicles, and the choice between these routes can be made based on the score of the resulting path length. Comparative simulations show their effectiveness over traditional methods. Further analysis shows that increasing the q-value reduces both path score and length, and that Einstein operators yield higher destination scores than Hamacher and Dombi, confirming the model’s adaptability and robustness.https://ieeexplore.ieee.org/document/10979912/Path optimization under uncertaintymulti-criteria path selectionq-rung orthopair fuzzy setsq-rung orthopair fuzzy directed graphsscore functionHamacher operators
spellingShingle Nazia Nazir
Tanzeela Shaheen
Wajid Ali
Md Rafiul Hassan
Mohammad Mehedi Hassan
Directed Fuzzy Edge Graphs Under q-ROF Environment: A Framework for Optimal Pathfinding
IEEE Access
Path optimization under uncertainty
multi-criteria path selection
q-rung orthopair fuzzy sets
q-rung orthopair fuzzy directed graphs
score function
Hamacher operators
title Directed Fuzzy Edge Graphs Under q-ROF Environment: A Framework for Optimal Pathfinding
title_full Directed Fuzzy Edge Graphs Under q-ROF Environment: A Framework for Optimal Pathfinding
title_fullStr Directed Fuzzy Edge Graphs Under q-ROF Environment: A Framework for Optimal Pathfinding
title_full_unstemmed Directed Fuzzy Edge Graphs Under q-ROF Environment: A Framework for Optimal Pathfinding
title_short Directed Fuzzy Edge Graphs Under q-ROF Environment: A Framework for Optimal Pathfinding
title_sort directed fuzzy edge graphs under q rof environment a framework for optimal pathfinding
topic Path optimization under uncertainty
multi-criteria path selection
q-rung orthopair fuzzy sets
q-rung orthopair fuzzy directed graphs
score function
Hamacher operators
url https://ieeexplore.ieee.org/document/10979912/
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AT mdrafiulhassan directedfuzzyedgegraphsunderqrofenvironmentaframeworkforoptimalpathfinding
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