Floyd’s Algorithm for All-Pairs Interval-Valued Neutrosophic Shortest Path Problems

Abstract

Neutrosophic set theory becomes an important tool in almost every real-world problems and therefore every field of mathematics taken the advantage of this theory. Present work is based on one of the classical problem of a branch of mathematics, known as graph theory. This subject contains the methods for finding minimal path of any network. Although, many algorithms are available for finding shortest path, but to increase its applicability in real-life problems, it is important to generalize it in those environments, which considers most of the real-life situations. In this work, we have generalized one of the popular algorithms, called Floyd’s algorithm using interval-valued neutrosophic set. The graph of five nodes is considered with the weights between them as interval-valued neutrosophic numbers, and the shortest path matrix is formed using the score function. The final score and transition path matrix provides the minimum value and the path between any pair of nodes.