A Greedy Algorithm for Fuzzy Shortest Path Problem using Quasi-Gaussian Fuzzy Weights

Several algorithms exist to determine the shortest path in a network for the crisp case where the weights are real numbers. In the real world, these weights represent parameters like cost, packet arrival time, link capacity etc which are not naturally precise. To model the uncertainty involved, for the first time we use the Gaussian fuzzy numbers as weights and a method has been presented in this paper to determine the fuzzy shortest path. Gaussian membership functions are preferred over other membership functions (triangular and trapezoidal) that are easy to analyze because it is continuous and differentiable enabling efficient gradient based optimization and it is simpler to represent because it requires fewer parameters. The issue of performing fuzzy arithmetic operations to calculate the fuzzy shortest path length and the corresponding fuzzy shortest path in the network has been addressed and to tackle it the concept of decomposed fuzzy numbers has been used. Also, a greedy algorithm which is an extension of Dijkstra’s algorithm for fuzzy shortest path problem has been proposed.