On Updating the Shortest Path in Fuzzy Graphs

There are some methods for finding the shortest path in fuzzy graphs. If the weight of an edge changes in the graph, the updated shortest path is calculated only by re-running the methods. In this paper, a new method to update the pre-calculated shortest path is presented which is definitely more efficient than completely re- executing the shortest path algorithm. Also, a new operator is defined that is indeed the generalized t- norm operator. To show method efficiency, a computer simulation is done. The simulation results are very promising. The upshots of this paper are based on the approach whose basic concepts and main outcomes are presented in the fuzzy shortest paths in fuzzy graphs given by Baniamerian and Menhaj (Computation Intelligence, Theory and Applications, Springer (2006), 757-764).