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###### Full Length Article
volume 11 , Issue1, PP: 53-61 , 2020

## Interval Valued Neutrosophic Shortest Path Problem by A* Algorithm

##### Authors Names :   S.Krishna Prabha   1 Said Broumi   2 Florentin Smarandache   3

1  Affiliation :  Department of Mathematics, PSNA College of Engineering and Technology, Dindigul-624622, Tamilnadu, India

Email :  jvprbh1@gmail.com

2  Affiliation :  Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, Casablanca, Morocco

Email :  broumisaid78@gmail.com

3  Affiliation :  Dept. Math and Sciences, University of New Mexico, Gallup, NM, USA

Email :  smarand@unm.edu

Doi   :  10.5281/zenodo.4127190

Received: Jun 09, 2020 Accepted: September 03, 2020

Abstract :

Many researchers have been proposing various algorithms to unravel different types of fuzzy shortest path problems. There are many algorithms like Dijkstra’s, Bellman-Ford,Floyd-Warshall and kruskal’s etc are existing for solving the shortest path problems. In this work a shortest path problem with interval valued neutrosophic numbers is investigated using the proposed algorithm. A* algorithm is extensively applied in pathfinding and graph traversal.Unlike the other algorithms mentioned above, A* algorithm entails heuristic function to uncover the cost of path that traverses through the particular state. In the structured  work A* algorithm is applied to unravel the length  of the shortest path by utilizing ranking function from the source node to the destination node. A* algorithm is executed by applying best first search with the help of this search, it greedily decides which vertex to investigate subsequently. A* is equally complete and optimal if an acceptable heuristic is concerned. The arc lengths in interval valued neutrosophic numbers are defuzzified using the score function.. A numerical example is used to illustrate the proposed approach.

Keywords :

Heuristic function , Interval Valued Neutrosophic Graph , Score Function , Shortest Path Problem. Destination node , Source node.

References :

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