Sensitivity analysis and application of single-valued neutrosophic transportaion problem

Abstract

The neutrosophic set serves as a powerful tool for addressing complexity, ambiguity, and managing imperfect and inconsistent information in the digital world. Graph theory plays a crucial role in determining the shortest path for neutrosophic sets through graph algorithms. This article introduces a novel algorithm, the bipartite graph contraction algorithm, to elucidate the graphical aspects within neutrosophic set theory by using score function for ranking. The proposed bipartite neutrosophic graph contraction algorithm is applied to solve a single-valued neutrosophic network, where the transportation unit cost is expressed as a trapezoidal single-valued neutrosophic number and produced the result as $〈\left(364,537,694,908\right);0.3,0.7,0.7〉$. A comparative analysis with an existing algorithm is conducted, and a novel introduction of sensitivity analysis in the realm of neutrosophic set theory is presented to assess the optimality of the result in neutrosophic transportation problems.