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A shortest path problem on a network with fuzzy arc lengths

✍ Scribed by Shinkoh Okada; Timothy Soper

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
187 KB
Volume
109
Category
Article
ISSN
0165-0114

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✦ Synopsis

We concentrate on a shortest path problem on a network in which a fuzzy number, instead of a real number, is assigned to each arc length. Introducing an order relation between fuzzy numbers based on "fuzzy min", a nondominated path or Pareto Optimal path from the speciΓΏed node to every other node is deΓΏned. 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 o ered 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.

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## Abstract In this work, we compute the distribution of __L__\*, the length of a shortest __(s, t)__ path, in a directed network __G__ with a source node __s__ and a sink node __t__ and whose arc lengths are independent, nonnegative, integer valued random variables having finite support. We constr