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.
Highlights
In order to overcome the real life situations which could not be handled in some conditions, Zadeh[1]introduced Fuzzy logic which was further developed by Zimmermann[2]
The rational subdivision of studying the nature, origins, and scope of neutralities, in addition to interface with a variety of ideational spectra is phrased as neutrosophy.The extension of neutrosophic set to neutrosophic offset, underset, and overset was proposed by Smarandache[3]
By using the score function Broumi et al [7] proposed an algorithm to solve the neutrosophic shortest path problem where the network arc lengths are represented by interval valued neutrosophic numbers
Summary
In order to overcome the real life situations which could not be handled in some conditions, Zadeh[1]. By using the score function Broumi et al [7] proposed an algorithm to solve the neutrosophic shortest path problem where the network arc lengths are represented by interval valued neutrosophic numbers. An Algorithm for shortest path problem in a network with interval valued intuitionstic trapezoidal fuzzy number was presented by Kumar et al.[11]. By defuzzifying the given interval valued neutrosophic cost by applying score function and by applying A* algorithm we find the optimal path. Let = (T1, I1, F1) be an interval valued neutrosophic number, the score function s( ) of an IVNN can be defined as follows:. Crisp valued neutroshopic shortest path problem Interval valued neutroshopic heuristic values to end nodes are given in the following table.
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