Calculation of Fuzzy shortest path problem using Multi-valued Neutrosophic number under fuzzy environment

• Published in: Neutrosophic sets and systems Vol. 57; pp. 356 - 369
• Main Authors: Raut, Prasanta Kumar, Behera, Siva Prasad, Broumi, Said, Mishra, Debdas
• Format: Journal Article
• Language: English
• Published: Neutrosophic Sets and Systems 01.09.2023; University of New Mexico
• Subjects: directed graph network; multi-valued neutrosophic numbers; selection sort technique; shortest path problem
• ISSN: 2331-6055; 2331-608X
• DOI: 10.5281/zenodo.8271401

The most well-known subject in graph theory is the shortest path problem (SPP), which has real-world applications in several different fields of study, including transportation, emergency services, network communications, fire station services, etc. The arc weights of the applicable SP problems are typically represented by fuzzy numbers in real-world applications. In this paper, we discussed the process of finding the shortest distance in a connected graph network in which the arc weights are multi-valued neutrosophic numbers (MNNs). Moreover, here we compare our method with some of the existing results and illustrate one implementation of our method with the help of one numerical example. Keywords: Directed graph network; Multi-valued neutrosophic numbers; selection sort technique; shortest path problem.