A genetic algorithm for solving fuzzy shortest path problems with mixed fuzzy arc lengths
We are concerned with the design of a model and an algorithm for computing the shortest path in a network having various types of fuzzy arc lengths. First, a new technique is devised for the addition of various fuzzy numbers in a path using alpha-cuts by proposing a least squares model to obtain membership functions for the considered additions. Due to the complexity of the addition of various fuzzy numbers for larger problems, a genetic algorithm is presented for finding the shortest path in the network. For this, we apply a recently proposed distance function for comparison of fuzzy numbers. Examples are worked out to illustrate the applicability of the proposed approach. (C) 2011 Elsevier Ltd. All rights reserved.
genetic algorithm shortest path fuzzy numbers alpha-cut regression model