An Innovative Approach to Solve Shortest Path Problem Using Dijkstra’s Algorithm Based on Interval-Valued Bipolar Neutrosophic Information

Abstract

The shortest path problem (SPP) is considerably important in several fields such as application in highway networks, the problem of scheduling, road transportation network, etc. The SPP focuses on recommending the path which has a minimum length enclosed by two vertices. The length of the arc represents real world measurements like cost, time, distance, price, or other
parameters. A neutrosophic set is a collection of the truth membership, indeterminacy membership, and falsity membership degrees of the elements. In an uncertain environment, neutrosophic numbers can express the arc distance more effectively. In this study, classical Dijkstra’s algorithm has been redesigned to handle the case in which most of the parameters of
a network are uncertain and given in terms of interval-valued bipolar neutrosophic numbers (IVBNN). The proposed algorithm gives the shortest path length using the score function from sources node to destination node and each of the arc lengths are attributed to an IVBNN. For the validation of the proposed algorithm, a numerical example has been conducted and the objective
of this study is to identify the optimal paths to rescue points. Finally, we describe the advantages of the proposed method and give some suggestions to further this study.