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.

Fuzzy efficiency evaluation in relational network data envelopment analysis: application in gas refineries

“…• Development of the proposed fuzzy relational NDEA model in the presence of undesirable outputs could be an interesting topic for future research. • The study can also be extended to many practical applications such as fuzzy transportation problem [6,7] and fuzzy shortest path problem [5,26,28,53]. • The proposed approach for fuzzy relational network DEA models in fuzzy environment can be developed for solving them in intuitionistic fuzzy environments [23] and intervalvalued fuzzy environments [17][18][19].…”

A Review: Current Trend of Immersive Technologies for Indoor Navigation and the Algorithms

“…Table 2 shows the types of shortest-path algorithms for indoor navigation, and Table 3 presents the types of deep-learning algorithms. Bellman-Ford algorithm for solving the shortest path problem of a network under a picture fuzzy environment (Parimala et al, 2021) 2021 Bellman-Ford The Bellman-Ford algorithm solves the shortest path issue under uncertainty in fuzzy image environments A study on the Bellman-Ford shortest path algorithm using a global positioning system (Rai, 2022) 2022…”

“…The presence or absence of the ability to walk along the edges in both directions distinguishes between a directed graph and an undirected graph. There are several different algorithms designed to solve the issue of the shortest path, including but not limited to Dijkstra's algorithm (P. , the Bellman-Ford algorithm (Parimala et al, 2021), the A* algorithm (Rachmawati & Gustin, 2020), the D* algorithm (Alves et al, 2019), and the Floyd-Warshall algorithm (Ramadiani et al, 2018).…”

Adaptive Sampling Path Planning for a 3D Marine Observation Platform Based on Evolutionary Deep Reinforcement Learning

“…Due to the complexity and temporal variability of the marine environment, as well as the diversity of autonomous underwater vehicle (AUV) planning tasks [6,7], adaptive sampling with MOPs requires efficient path-planning technology to ensure the smooth completion of tasks. Algorithms currently applied in path planning include the Dijkstra [8], Bellman Ford [9], Floyd-Warshall [10], A-star [11], Dynamic Programming [12], Artificial Potential Field [13], and Linear Quadratic [14] algorithms. Heuristic algorithms have also been applied, including the Genetic [15], Ant Colony [16], and Particle Swarm Optimization [17] algorithms.…”