Heuristic Incident Edge Path Algorithm for Interval-Valued Neutrosophic Transportation Network (Contemporary Mathematics, 2024)
Neutrosophic Set is an extension of Fuzzy set theory dealts with uncertain environments in Transportation, Decision-making etc. Finding the shortest path for an uncertain environment is one of the most challenging tasks, many heuristic algorithms play a vital role in releasing this task. This research article an heuristic algorithmic approach using graph theoretical methods helps the researcher to crack the challenge and which type of algorithm can use the type of score functions are discussed. Especially, the interval-valued Neutrosophic transportation problem (IVNTP) is considered for finding the shortest path which is a real-world decision-making problem in an ambiguous (uncertain) environment. Providing the shortest and finest way to address this ambiguity leads to the success of researcher to the organization. The algorithm used has been introduced for determination of interval-valued Neutrosophic shortest path (IVNSP) from the origin node to all other nodes by de-neutrosophicated edges using score functions. An illustrative Interval-valued neutrosophic transportation problem explains the algorithm’s efficacy and authenticity to find optimum result; this research article discusses about the nature of score functions, and some score function were taken into consideration. Further, the heuristic algorithm used is applicable for both positive and negative weighted edges; it was elaborated and compared with existing algorithm results, and it also provided all pair of shortest path. Future study and brief study of this article was disclosed in conclusion.
Keywords: score function, interval-valued neutrosophic number, ranking, de-neutrosophicated number, interval-valued neutrosophic shortest path problem