Abstract
The shortest path problem is a topic of increasing interest in various scientific fields. The damage to roads and bridges caused by disasters makes traffic routes that can be accurately expressed become indeterminate. A neutrosophic set is a collection of the truth membership, indeterminacy membership, and falsity membership of the constituent elements. It has a symmetric form and indeterminacy membership is their axis of symmetry. In uncertain environments, the neutrosophic number can more effectively express the edge distance. The objectives in this study are to solve the shortest path problem of the neutrosophic graph with an edge distance expressed using trapezoidal fuzzy neutrosophic numbers (TrFNN) and resolve the edge distance according to the score and exact functions based on the TrFNN. Accordingly, the use of a circle-breaking algorithm is proposed to solve the shortest path problem and estimate the shortest distance. The feasibility of this method is verified based on two examples, and the rationality and effectiveness of the approach are evaluated by comparing it with the Dijkstra and Bellman algorithms.
Highlights
The shortest path problem (SPP) is a topic of significant interest in various scientific fields pertaining to flow in additive networks
According to the geographical location and terrain, the degree of damage is classified based on the disaster and other factors, and the edge distance is represented as a trapezoidal fuzzy neutrosophic numbers (TrFNN) e n, where node i is the parent node and node j is the child node
We developed a circle-breaking algorithm for solving the SPP of a trapezoidal fuzzy neutrosophic graph and verified the feasibility of the algorithm using an example
Summary
The shortest path problem (SPP) is a topic of significant interest in various scientific fields pertaining to flow in additive networks. Deli [23] presented detailed work on the expansion and contraction of the conventional neutrosophic soft set and later [24] proposed single-valued trapezoidal neutrosophic operators and applied these to decision-making problems. Deli and Şubaş [25] proposed weighted geometric operators with single-valued triangular NN and applied these to decision-making problems. Broumi used the original Bellman algorithm to search the shortest path from the start point to the end point, whereas Tan used the improved dynamic programming algorithm for application to the SPP of a trapezoidal fuzzy medium intelligence graph, starting the search from the end point, and the NN was not accurate in the operation process. Yang et al [35] developed an ant colony algorithm for solving the SPP on a network with interval-valued neutrosophic edge distances. The shortest path solution method in neutrosophic graphs is evaluated in this study based on the circle-breaking algorithm
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