Constraint Shortest Path Problem in a Network with Intuitionistic Fuzzy Arc Weights

Abstract

The Shortest Path (SP) problem is one of the most widely used problems in network optimization which has a wide range of applications in various fields of science and engineering such as communication, transportation, routing and scheduling. The aim of this problem is to find a minimum cost path between two specified nodes. In the present communication, we consider a modified version of the SP known as constraint SP (CSP) problem with an additional constraint that establishes an upper limit on the travel time for the path. The objective of the CSP problem is to determine a minimum cost path between two specified nodes that the traversal time of the path does not exceed from a specified time. Traditional CSP problems assume the arc weights represented by time and cost are specified precisely. However, these weights can fluctuate with traffic conditions, weather, or payload. For this reason, being able to deal with vague and imprecise data may greatly contribute to the application of CSP problems. Here, we first formulate a CSP problem in a directed network where the arc weights represented by cost and time are intuitionistic trapezoidal fuzzy numbers. We then develop an approach for solving the intuitionistic fuzzy CSP problem under consideration. Finally, we present a small numerical example to illustrate the proposed approach.