[1] Liu Chunlin**, He Jianmin, Shi Jianjun,. New Methods to Solve Fuzzy Shortest Path Problems* [J]. Journal of Southeast University (English Edition), 2001, 17 (1): 18-21. [doi:10.3969/j.issn.1003-7985.2001.01.005]

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New Methods to Solve Fuzzy Shortest Path Problems^*()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

17

Issue:

2001 1

Page:

18-21

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2001-06-30

Info

Title:

New Methods to Solve Fuzzy Shortest Path Problems^*

Author(s):

Liu Chunlin^1**;  He Jianmin²;  Shi Jianjun¹

¹Business School, Nanjing University, Nanjing 210093, China
²College of Economics and Management, Southeast University, Nanjing 210096, China

Keywords:

triangular fuzzy number;  fuzzy shortest path;  ranking function

PACS:

O221.2

DOI:

10.3969/j.issn.1003-7985.2001.01.005

Abstract:

This paper discusses the problem of finding a shortest path from a fixed origin s to a specified node t in a network with arcs represented as typical triangular fuzzy numbers(TFN). Because of the characteristic of TFNs, the length of any path p from s to t, which equals the extended sum of all arcs belonging to p, is also TFN. Therefore, the fuzzy shortest path problem(FSPP)becomes to select the smallest among all those TFNs corresponding to different paths from s to t(specifically, the smallest TFN represents the shortest path). Based on Adamo’ s method for ranking fuzzy number, the pessimistic method and its extensions — optimistic method and λ-combination method, are presented, and the FSPP is finally converted into the crisp shortest path problems.

References:

[1] C.M. Klein, Fuzzy shortest paths, Fuzzy Sets and Systems, vol.39, pp. 27-41, 1991
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[3] Y.L.Chen, and K.Tang, Shortest paths in time-schedule networks, Internat. J. Operations and Quantitative Management, vol.3, no.1, pp. 157-173, 1997
[4] Y. Hadas, and A. Ceder, Shortest path of emergency vehicles under uncertain urban traffic conditions, Transportation Research Record, vol.11, no.1, pp. 34-39, 1996
[5] S.Okada, and M.Gen, Fuzzy shortest path problem, Computers Industrial Engineering, vol. 27, no.4, pp. 465-468, 1994
[6] G.Facchinetti, R.G.Ricci, and S.Muzzioli, Note on ranking fuzzy triangular numbers, Internat. J. Intelligent Systems, vol.13, no. 4, pp.613-622, 1998
[7] S.Okada, and M.Gen, Order Relation between intervals and its application to shortest path 0problem, Computers Industrial Engineering, vol. 25, no.1, pp.147-150, 1994
[8] J.M.Adamo, Fuzzy decision trees, Fuzzy Sets and Systems, vol. 4, pp. 207-219, 1980
[9] S.M.Baas, and H.Kwakernaak, Rating and ranking of multiple-aspect alternatives using fuzzy sets, Automatica, vol.13, no.1, pp. 47-58, 1977
[10] J.F.Baldwin, and N.C.F. Guild, Comparison of fuzzy sets on the same decision space, Fuzzy Sets and Systems, vol.2, no.1, pp. 213-233, 1979
[11] G.Bortolan, and R.Degani, A review of some methods for ranking fuzzy subsets, Fuzzy Sets and Systems, vol.15, pp.1-19, 1985

Memo

Memo:

* The project supported by the National Nature Science Foundation of China(79970096).
** Born in 1970, male, doctor.

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