A shortest-path network problem in a fuzzy environment

This paper investigates a shortest-path network problem in a fuzzy environment. We assume that the edge weight of the network is not known exactly and only estimated values are given. This leads to the use of fuzzy numbers for representing imprecise data values. The main results obtained from this study are as follows: (1) using triangular fuzzy numbers and a signed distance ranking method to obtain Theorem 1- a shortest-path network problem in a fuzzy environment; (2) the shortest path obtained from Theorem 1 corresponds to the actual path in the non-fuzzy network; and (3) the fuzzy shortest-path problem is an extension of the crisp problem