Evaluation of Shortest Path by using Breadth-First Algorithm under Neutrosophic Environment

Abstract

This paper recommends and designs concepts for evaluating the shortest path (SP) for a connected network using a modified breadth-first search algorithm in an uncertain environment. Evaluating the SPs of a network is an essential and extensively encountered optimization problem. Here we develop a new method for determining the SP in a neutrosophic environment in which the arc lengths are uncertain. Here, we use the parameters as neutrosophic numbers, and the new methodology, i.e., canonical representation of neutrosophic numbers in a neutrosophic environment, is used to convert neutrosophic edge lengths to crisp edge lengths and enhance the traditional breadth-first search algorithm. We employ this concept to accommodate the ambiguities in subjective decisions and address these issues. Here we demonstrate that the proposed algorithm has good stability and high efficiency for evaluating the SP. Finally, a numerical example is provided to explain the suggested algorithm.