The shortest path algorithm is one of the best choices for implementation of data structures. The shortest path (SP) problem involves the problem of finding a suitable path between “two vertices or nodes in a graph” in such a way that the sum of the weights of its component edges is minimal. There are many theories for solving this problem one of the widely used way solution for solving this problem is Dijkstra’s algorithm (DA) which is also widely used in many engineering calculation works also. There are two types of DA one is the basic one and other one is optimized. This paper is focused on the basics one which provides a shortest route between source node and the destination node. Main focus has been kept on keeping the work simple and easy to understand with some basic concepts .Storage space and operational efficiency improvement has been tried to improve.
An approach to data processing for relational databases is called a rough set theory. It is an interesting area of uncertainty mathematics that is mainly related to fuzzy theory. Rough set theory and neutrosophic set theory can be joined to create a powerful tool for dealing with indeterminacy. Neutrosophic matrices help decision-makers deal with multi-criteria decisionmaking by providing them with more useful and practical when we apply the concept of matrix energy. In this paper, we defined a Rough neutrosophic matrix and its energy. Some propositions, lower and upper limits of the rough neutrosophic matrix's energy were derived. The proposed energy of the rough neutrosophic matrix was applied in multi-criteria decision-making problems. The problem is to select the best place for constructing the school building. Applying the energy method to the MCDM problem became more relatable and produced good results.
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