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Fuzzy Dijkstra algorithm for shortest path problem under uncertain environment |
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| Authors: | Yong Deng Yuxin ChenYajuan Zhang Sankaran Mahadevan |
| Affiliation: | a School of Computer and Information Sciences, Southwest University, Chongqing 400715, China b School of Electronics and Information Technology, Shanghai Jiao Tong University, Shanghai 200240, China c School of Engineering, Vanderbilt University, Nashville, TN 37235, USA |
| Abstract: | A common algorithm to solve the shortest path problem (SPP) is the Dijkstra algorithm. In this paper, a generalized Dijkstra algorithm is proposed to handle SPP in an uncertain environment. Two key issues need to be addressed in SPP with fuzzy parameters. One is how to determine the addition of two edges. The other is how to compare the distance between two different paths with their edge lengths represented by fuzzy numbers. To solve these problems, the graded mean integration representation of fuzzy numbers is adopted to improve the classical Dijkstra algorithm. A numerical example of a transportation network is used to illustrate the efficiency of the proposed method. |
| Keywords: | Shortest path problem Dijkstra algorithm Fuzzy numbers Graded mean representation |
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