The shortest path problem is an important classical network optimization problem arising from many
applications. In many cases, however, some aspects of a network-theoretic problem may be uncertain.
For example, the vehicle travel time or vehicle capacity on a road network may not be known exactly.
In such cases, it is natural to deal with the uncertainty using fuzzy set theory. Here, we consider solving
the All-Pairs Shortest Paths Problem (APSPP) in a network with fuzzy arc lengths. Making use of a
suitable ranking method, we propose a new approach to solve the fuzzy APSPP using a genetic
algorithm. Illustrative examples are worked out to demonstrate our proposed method.
