DETERMINATION OF THE SHORTEST PATH IN VAGUE NETWORKS

Abstract

We propose a new approach to determine the shortest path in a vague network(VN), a network in which vertices and edges remain crisp but each edge (i,i+1) has an associated weight, which is a vague number of the form [R_it,R_if] for each i.  For each VN, we associate two vague networks called true and false limit fuzzy networks having the same set of vertices and edges but each edge (i,i+1) is attached with a vague weight R_it and R_if respectively.  We exhibit that the shortest path of weight w = [w_t,w_f] an vague number in VN, the path for which the shortest path of weight w_t in the true fuzzy network coincides with the shortest path of weight wt in the true limit vague network.  The concept is illustrated with the help of a simple situation and the validation of mathematical verification is provided.