A shortest path problem on a network with fuzzy arc lengths

We concentrate on a shortest path problem on a network in which a fuzzy number, instead of a real number, is assigned to each are length. Introducing an order relation between fuzzy numbers based on "fuzzy min", a nondominated path or Pareto Optimal path from the specified node to every other node is defined. An algorithm for solving the problem is developed on the basis of the multiple labeling method for a multicriteria shortest path. As a result, a number of nondominated paths can be obtained and is offered to a decision maker. However, a number of nondominated paths derived from large scale network may be too numerous for him to choose a preferable path. Due to this situation, we propose a method to reduce the number of paths according to a possibility level. The proposed algorithm is numerically evaluated on large scale random networks. (C) 2000 Elsevier Science B.V. All rights reserved.