Application of neutrosophic minimum spanning tree in electrical power distribution network

Abstract

The problem of finding the minimum spanning tree (MST) is one of the most studied and importantcombinatorial optimisation problems in graph theory. Several types of uncertainties exist in real-life problems, whichmake it very hard to find the exact length of the arc. The neutrosophic set is an efficient tool to model and deal withthe uncertainties in information due to inconsistent and indeterminate. In this study, the authors use triangularneutrosophic numbers to represent the edge weights of a neutrosophic graph for the MST problem in the neutrosophicenvironment. They call this problem a neutrosophic MST (NMST) problem. They formulate the NMST problem interms of the linear programming model. Here, they introduce an algorithmic method based on a genetic algorithm forsolving the NMST problem. They present the utility of triangular neutrosophic numbers as edge weights and theirapplication in the electrical distribution network.