Abstract
Shortest path problem is a fundamental problem in network optimization and combinational optimization. The existing literature mainly concerned with the problem in deterministic, stochastic or fuzzy environments by using different tools. Different from the existing works, we investigate shortest path problem by regarding arc lengths as uncertain variables which are employed to describe the behavior of uncertain phenomena. According to different decision criteria, three concepts of path are proposed in uncertain environment, and three types of uncertain programming models are formulated. Furthermore, these models are concerted into deterministic optimization models in several special cases.
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References
1. Chen XW, Liu B (2012) Existence and uniqueness theorem for uncertain differential equations. Fuzzy Optimization and Decision Making, to be published
2. Dubois D, Prade H (1980) Fuzzy sets and systems: Theory and applications. Academic Press, New York
3. Frank H (1969) Shortest paths in probability graphs. Operations Research 17:583–599
4. Fu L, Rilett LR (1998) Expected shortest paths in dynamic and stochstic traffic networks. Transportation Sciences 32:499–516
5. Hernandes F, Lamata MT, Verdegay JL et al (2007) The shortest path problem on networks with fuzzy parameters. Fuzzy Sets and Systems 158:1561–1570
6. Ji X, Iwamura K, Shao Z (2007) New models for shortest path problem with fuzzy arc lengths. Applied Mathematical Modelling 31:259–269
7. Keshavarz E, Khorram E (2009) A fuzzy shortest path with the highest reliability. Journal of Compuational and Applied Mathematics 230:204–212
8. Klein CM (1991) Fuzzy shortest paths. Fuzzy Sets and Systems 39:27–41
9. Li X, Liu B (2009) Hybrid logic and uncertain logic. Journal of Uncertain Systems 3:83–94
10. Lin K, Chen M (1994) The fuzzy shortest path problem and its most vital arcs. Fuzzy Sets and Systems 38:343–353
11. Liu B (2007) Uncertainty theory. 2nd edn, Springer-Verlag, Berlin 2007. 502 W. Liu
12. Liu B (2009) Some research problems in uncertainty theory. Journal of Uncertain Systems 3:3–10
13. Moazeni S (2006) Fuzzy shortest path problem with finite fuzzy quantities. Applied Mathematics and Computaion 183:160–169
14. Murthy I, Sarkar S (1996) A relaxation-based pruning technique for a class of stochastic shortest path problems. Transportation Sciences 30:220–236
15. Ohtsubo Y (2008) Stochastic shortest path problems with associative accumulative criteria. Applied Mathematics and Computation 198:198–208
16. Okada S (2004) Fuzzy shortest path problems incorporting interactivity among paths. Fuzzy Sets and Systems 142:335–357
17. Okada S, Soper T (2000) A shortest path problem on a network with fuzzy arc lengths. Fuzzy Sets and Systems 109:129–140
18. Qin Z (2009) On lognormal uncertain variables. In: Proceedings of the Eighth International Conference on Information and Management Sciences 753–755
19. Qin Z (2009) Developments of conditional uncertain measure. In: Proceedings of the Eighth International Conference on Information and Management Sciences 782–786
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Liu, W. (2013). Optimization Models for Shortest Path Problem with Stochastic Arc Lengths Taking Fuzzy Information. In: Xu, J., Yasinzai, M., Lev, B. (eds) Proceedings of the Sixth International Conference on Management Science and Engineering Management. Lecture Notes in Electrical Engineering, vol 185. Springer, London. https://doi.org/10.1007/978-1-4471-4600-1_43
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DOI: https://doi.org/10.1007/978-1-4471-4600-1_43
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