Bellman–Ford algorithm for solving shortest path problem of a network under picture fuzzy environment

Abstract

An elongation of the novel intuitionistic fuzzy set is a picture fuzzy set theory. The demonstration of this has been used to deal with the abstinence criteria in a decision-making problem. The uncertainty in nature occurs sometimes in real-world problems and amidst them, the prominent one is the shortest path problem (SPP) solving. In the last few years, one of the best algorithms on the network for finding SPP is Bellman–Ford. Due to uncertainty in the decision-making process, it becomes difficult for decision-makers for communicating their point of view and judgment with certainty. We conceive of SPP in this contribution via Bellman's algorithm (BA) for a network with trapezoidal picture fuzzy numbers (TPFNs). We introduce a new algorithm to stand the shortest picture fuzzy path between each pair of nodes. A TPFN is considered for the length of all edges. A numerical example for the validation of the presented algorithm has also been proposed. There has also been relative research with existing techniques showing the benefits of the new algorithm.