Introduction
In this chapter we consider the shortest route problem where distances/costs are not known precisely and are modeled using fuzzy numbers. The fuzzy shortest route problem is outlined in the next section. We have previously used an evolutionary algorithm to solve an example problem (Section 6.5.1 of [2] and [3]). In Section 18.3 we plan to apply our fuzzy Monte Carlo method to obtain a solution to this example problem and then compare both solution methods.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Boulmakoul, A.: Generalized Path-Finding Algorithms on Semirings and the Fuzzy Shortest Path Problem. J. Computational and Applied Mathematics 162, 263–272 (2004)
Buckley, J.J., Eslami, E., Feuring, T.: Fuzzy Mathematics in Economics and Engineering. Physica-Verlag, Heidelberg (2002)
Buckley, J.J., Feuring, T., Hayashi, Y.: Solving Fuzzy Problems: Operations Research. J. Advanced Computational Intelligence 3, 171–176 (1999)
Chuang, T.-N., Kung, J.-Y.: The Fuzzy Shortest Path Length and the Corresponding Shortest Path in a Network. Computers and Operations Research 32, 1409–1428 (2005)
Cornelis, C., DeKesel, P., Kerre, E.E.: Shortest Paths in Fuzzy Weighted Graphs. Int. J. Intelligent Systems 19, 1051–1068 (2004)
Hernandes, F., Lamata, M.T., Verdegay, J.L., Yamakami, A.: The Shortest Path Problem on Networks with Fuzzy Parameters. Fuzzy Sets and Systems 158, 1561–1570 (2007)
Itoh, T., Ishii, H.: A Model of Fuzzy Shortest Path by Possibility Measure. Japanese J. of Fuzzy Theory and Systems 8, 977–990 (1996)
Ji, X., Iwamura, K., Shao, Z.: New Models for Shortest Path Problem with Fuzzy Arc Lengths. Applied Math. Modeling 31, 259–269 (2007)
Lin, K.-C., Chern, M.-S.: The Fuzzy Shortest Path Problem and Its Most Vital Arcs. Fuzzy Sets and Systems 58, 343–353 (1993)
Malik, D.S., Mordeson, J.N.: Fuzzy Discrete Structures. Springer, Heidelberg (2000)
Okada, S.: Fuzzy Shortest Path Problems Incorporating Interactivity Among Paths. Fuzzy Sets and Systems 142, 335–357 (2004)
Okada, S., Soper, T.: A Shortest Path Problem on a Network with Fuzzy Arc Lengths. Fuzzy Sets and Systems 109, 129–140 (2000)
Shih, H.-S., Lee, E.S.: Fuzzy Multi-Level Minimum Cost Flow Problem. Fuzzy Sets and Systems 107, 159–176 (1999)
Yao, J.-S., Lin, F.-T.: Fuzzy Shortest-Path Network Problems with Uncertain Edge Weights. J. Information Science and Engineering 19, 329–351 (2003)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Buckley, J.J., Jowers, L.J. (2007). Fuzzy Shortest Path Problem. In: Monte Carlo Methods in Fuzzy Optimization. Studies in Fuzziness and Soft Computing, vol 222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76290-4_18
Download citation
DOI: https://doi.org/10.1007/978-3-540-76290-4_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-76289-8
Online ISBN: 978-3-540-76290-4
eBook Packages: EngineeringEngineering (R0)