Fuzzy Dijkstra algorithm for shortest path problem under uncertain environment

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.

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► We model two hospitals which have regulated prices and compete on quality.
► We examine changes in the level of information about hospital quality.
► Increasing information will increase quality if hospital costs are similar.
► Increasing information will decrease quality if hospital costs are very different.
► Welfare effects depend on ex-ante or ex-post assumptions about quality information.