An efficient algorithm to shortest path problems onfuzzy graphs

The shortest path problem is the one of earliest combinatorial optimization problems, in whichthe decision maker wishes to nd a path from an origin to a destination in a way that the total lengthis minimized. This paper addresses a natural extension of the problem, in which the underlying graphis a fuzzy graph. This extension is meaningful in some applicable situations that there are one expert'sopinions about the relative importance of arcs or nodes. The goal of the decision maker is to make adecision not only regrading the lengths, but also the expert's opinions. This paper concentrates on solvingthis problem in fuzzy environment. It rst models the problem as a tri-objective optimization. Then, the-constraint method is applied to propose an ecient algorithm for nding a satisfactory solution.

کلیدواژه ها:

shortest path problem ، fuzzy graphs ، satisfactory solution.