ESMAILE KESHAVARZ
ESMAILE KHORRAM

In this paper a network with triangular fuzzy arc lengths is considered, and then a tree of shortest paths between a specified source node and other nodes of the network is obtained. This problem is ill-posed because it can not be determined whether an arc locates on the shortest path, or not. Then, on basis of the possibility theory, we defined the degree of possibility that an arc is on the tree of shortest paths. In presented definition of degree of possibility interactivity terminology is used in order to compare different additions of fuzzy numbers and also lengths of twodistinct specified paths. Next, an algorithm is presented with the intention of assess degree of possibility of each arc and also with the aim of achievement a tree that contains those arcs which have the highest degree of possibility. Finally, an illustrative example is given to demonstrate the proposed algorithm

Fuzzy numbers; Possibility theory; Tree of shortest paths; Degree of possibility; Interactivity