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 α -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 propose a new
approach to solve the fuzzy all pairs shortest path problem using a genetic algorithm. Examples are worked out to
illustrate the applicability of the proposed model.
