Fuzzy Dijkstra Algorithm to Find the Shortest Path

Abstract

Shortest path for crisp numbers can be found efficiently using the Dijkstra’s algorithm. There are some uncertain conditions in the environment which introduces a fuzzy number for the distances between two nodes. A classical Dijkstra algorithm is modified to fuzzy Dijkstra algorithm to address the problem. Graded mean integration is used to enhance the algorithm by calculating and comparing the path length between two nodes when the arc length is fuzzy. A sample network is shown to understand the shortest path for fuzzy numbers. Key Words: dijkstra’s algorithm, fuzzy numbers, graded mean integration