A matrix approach for minimum spanning tree in neutrosophic and application in medical waste management / Nur Haifa Ahmad Hayazim, Siti Nurain Zulkifli and Siti Nurhidayah Yaacob

The problem of finding the minimum spanning tree (MST) is one of the most extensively studied and significant combinatorial optimization problems in graph theory. Many research works have been done to find an MST due to its various applications. In real-life problems, there are a variety of uncertainties that make determining the exact length of the arc extremely difficult. The neutrosophic set is a useful tool for modeling and dealing with information uncertainties caused by inconsistent and indeterminate data. The aim of this study is to propose a matrix al-gorithm for finding MST in the environmentof undirected interval-valued bipolar neutrosophic (TVBN) connected graphs. The weights are assigned to each edge in the form of an IVBN number. The use of IVBN improves the realistic aspects of the problem as it can describe the uncertainty, indeterminacy, and hesitancy of the real world better. A numerical example related to finding the optimal route that can minimize the cost of solving the medical waste management is provided to show the effectiveness of the Prim's and Kruskal's algorithms with IVBN. As a final step, a comparative study such as interval-valued neutrosophic minimum spanning tree (IVN-MST), interval-valued intuitionistic fuzzy minimum spanning tree (IVIF-MST) and interval-valued fuzzy minimum spanning tree (IVE-MST) is presented to point out the advantages of the proposed method over that of other existing algorithms. As a result, the IVBN set is a better solution for solving the problem of MST.