A Novel Method for Solving the Time-Dependent Shortest Path  Problem under Bipolar Neutrosophic Fuzzy Arc Values

Vidhya K; Saraswathi A; Broumi Said

A Novel Method for Solving the Time-Dependent Shortest Path Problem under Bipolar Neutrosophic Fuzzy Arc Values

Authors

Vidhya K Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Chengalpattu 603203,TamilNadu,India;
Saraswathi A Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Chengalpattu 603203,TamilNadu,India;
Broumi Said 3Faculty of Science Ben MSik, University Hassan II, Casablanca, Morocco;

Keywords:

Shortest Path Problem; Bipolar Neutrosophic Fuzzy Arc Weights; Bellman-ford Algorithm; Time dependent Shortest path problem.

Abstract

The Shortest path problem is highly relevant in our daily lives, addressing uncertainties like traffic
conditions and weather variations. To handle such uncertainties, we utilize Fuzzy Numbers. This paper focuses
on Bipolar Neutrosophic Fuzzy Numbers, which have dual positive and negative aspects. They provide a
robust framework for representing arc (node/edge) weights, signifying uncertain travel times between nodes.
Importantly, these weights can change over time in bipolar neutrosophic fuzzy graphs. Our study introduces
an extended Bellman-Ford Algorithm for identifying optimal paths and minimum times with time-dependent
Bipolar Neutrosophic Fuzzy arc weights. We demonstrate its effectiveness through a step-by-step numerical
example and conduct a comparative analysis to evaluate its efficiency.

DOI: 10.5281/zenodo.10795555

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Published

2024-03-01

Issue

Vol. 65 (2024): Neutrosophic Sets and Systems

Section

Article

License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Creative Commons Attribution (CC BY) license.

How to Cite

Vidhya K, Saraswathi A, & Broumi Said. (2024). A Novel Method for Solving the Time-Dependent Shortest Path Problem under Bipolar Neutrosophic Fuzzy Arc Values. Neutrosophic Sets and Systems, 65, 80-100. https://fs.unm.edu/nss8/index.php/111/article/view/4297