Article: Solving fuzzy shortest path problem with vertex transfer penalties under type-2 fuzzy environment Journal: International Journal of Mathematics in Operational Research (IJMOR) 2024 Vol.28 No.4 pp.526 - 548 Abstract: Shortest path problems have many applications in the field of graph theory. However, the traditional shortest path algorithms only work in a situation where an edge penalty is a real number. In real-world situations like the shipping and transportation industry, the edge weight from a source node to the destination node often could not be defined through a real number due to incompleteness or inexactness, this can be challenging in some cases and can be defined through a fuzzy number. In this scenario, finding the shortest path between two nodes has already been solved in the past. In this paper, we are trying to find the shortest path between two nodes where the graph has transfer penalties at the node and the transfer penalties are defined by a type-2 trapezoidal fuzzy number. This problem has a go-to solution, i.e., to use a Kirby-Potts expansion to add parallel edges and then use the standard Dijkstra algorithm to find the shortest path. In this paper, we have not used any graph extension technique, but we have used a modified Dijkstra algorithm to manage the vertex penalty and find the shortest path in between the nodes. A numerical example is provided to explain the usefulness of the approach. Inderscience Publishers - linking academia, business and industry through research

Title: Solving fuzzy shortest path problem with vertex transfer penalties under type-2 fuzzy environment

Authors: Babita Chaini; Narmada Ranarahu

Addresses: Department of Mathematics, Institute of Technical Education and Research, Siksha 'O' Anusandhan University, Bhubaneswar, India ' Department of Mathematics, Institute of Technical Education and Research, Siksha 'O' Anusandhan University, Bhubaneswar, India

Abstract: Shortest path problems have many applications in the field of graph theory. However, the traditional shortest path algorithms only work in a situation where an edge penalty is a real number. In real-world situations like the shipping and transportation industry, the edge weight from a source node to the destination node often could not be defined through a real number due to incompleteness or inexactness, this can be challenging in some cases and can be defined through a fuzzy number. In this scenario, finding the shortest path between two nodes has already been solved in the past. In this paper, we are trying to find the shortest path between two nodes where the graph has transfer penalties at the node and the transfer penalties are defined by a type-2 trapezoidal fuzzy number. This problem has a go-to solution, i.e., to use a Kirby-Potts expansion to add parallel edges and then use the standard Dijkstra algorithm to find the shortest path. In this paper, we have not used any graph extension technique, but we have used a modified Dijkstra algorithm to manage the vertex penalty and find the shortest path in between the nodes. A numerical example is provided to explain the usefulness of the approach.

Keywords: fuzzy shortest path problems; IT2TrFN; modified Dijkstra algorithm; transfer penalties.

DOI: 10.1504/IJMOR.2024.140352

International Journal of Mathematics in Operational Research, 2024 Vol.28 No.4, pp.526 - 548

Received: 10 Aug 2022
Accepted: 05 Apr 2023
Published online: 05 Aug 2024 *

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Title: Solving fuzzy shortest path problem with vertex transfer penalties under type-2 fuzzy environment

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