Computing a fuzzy shortest path in a network with mixed fuzzy arc lengths using $\alpha$-cuts

Abstract

We are concerned with the design of a model and an algorithm for computing a shortest path in a network having various types of fuzzy arc lengths. First, we develop a new technique for the addition of various fuzzy numbers in a path using $\alpha$-cuts by proposing a linear least squares model to obtain membership functions for the considered additions. Then, using a recently proposed distance function for comparison of fuzzy numbers, we present a dynamic programming method for finding a shortest path in the network. Examples are worked out to illustrate the applicability of the proposed model.