• Determination of the Shortest Path in Interval Valued Fuzzy Networks

Abstract

We propose a new approach to determine the shortest path in an Interval valued fuzzy networks (IVFN), a network in which vertices (or nodes) and edges (or links) remain crisp but each edge (i, i+1) has an associated weight, which is an interval fuzzy number of the form Ri = [RiL, RiU] for each i. For each IVFN, we associate two fuzzy networks called lower and upper limit fuzzy networks having the same set of vertices and edges but each edge(i, i+1) is attached with a fuzzy weight RiL and RiU respectively. We exhibit that the shortest path of weight w = [wL, wU] an interval fuzzy number in IVFN, is that path for which the shortest path of weight wL in the lower limit fuzzy network coincides with the shortest path of weight wU in the upper limit fuzzy network. The concept is illustrated with the help of a simple situation and the validation of mathematical verification is provided.