Fuzzy constrained shortest path algorithm using circumcenter of centroids

Abstract

The constrained shortest path problem (CSPP) is a well known NP-Complete problem where the task is to determine the shortest path that satisfies certain constrains like delay and cost. Other than the straight-forward implementation in the area of networking, this problem also finds application in the field of multimedia, crew scheduling etc. In these kinds of applications it is important to take into consideration the uncertainty involved in the network environment to provide the Quality of Service (QoS) assurance which can be modeled by the use of fuzzy numbers for the representation of the parameters involved. In this paper, we extend the algorithm stated by Sahni et al to deal with the fuzzy constrained shortest path problem (FCSPP) by fuzzifying one of the constraints i.e. cost and representing it as a trapezoidal fuzzy number. Fuzzy numbers cannot be ordered like real numbers so the Circumcenter of Centroid method is used to rank the trapezoidal fuzzy numbers and determine the fuzzy constrained shortest path also taking into account the delay involved.