Solving fuzzy shortest path problem with vertex transfer penalties under type-2 fuzzy environment
by Babita Chaini; Narmada Ranarahu
International Journal of Mathematics in Operational Research (IJMOR), Vol. 28, No. 4, 2024

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.

Online publication date: Mon, 05-Aug-2024

The full text of this article is only available to individual subscribers or to users at subscribing institutions.

 
Existing subscribers:
Go to Inderscience Online Journals to access the Full Text of this article.

Pay per view:
If you are not a subscriber and you just want to read the full contents of this article, buy online access here.

Complimentary Subscribers, Editors or Members of the Editorial Board of the International Journal of Mathematics in Operational Research (IJMOR):
Login with your Inderscience username and password:

Username:        Password:          Forgotten your password?

Want to subscribe?
A subscription gives you complete access to all articles in the current issue, as well as to all articles in the previous three years (where applicable). See our Orders page to subscribe.

If you still need assistance, please email subs@inderscience.com