An improved \(A^*\) search algorithm for the shortest path under interval-valued Pythagorean fuzzy environment

The Shortest Path Problem is one of the most exciting topics in network optimization graph theory and is also used in various applications, such as transportation, Internet Protocol routing, Robotic Path, Emergency services, etc. In most real-world applications, the values will not be precise.To deal with imprecise issues, a fuzzy environment was chosen. The shortest path problem is formulated in this paper for an extended A* search algorithm under interval-valued Pythagorean Fuzzy Environment. The main objectives of this work are (i) find an optimal path using interval-valued pythagorean numbers, (ii) the heuristic methods are used to be flexible and to find quick decisions, and these values are calculated using reversal breadth-first search under interval-valued pythagorean numbers, (iii) an improved accuracy function is used to compare and find the minimum cost and to label the nodes, (iv) the results are compared with existing methods and analyzed. From this study it is observed that the proposed method provides the best optimal cost and the shortest path among the available techniques and thus may be implemented to identify a practical situation in a fuzzy environment.