A dynamic programming approach for finding shortest chains in a fuzzy network

Applied Soft Computing Journal

Volumn 9, Issue 2, 2009, Pages 503-511

  Mahdavi, Iraj ^a   Nourifar, Rahele ^b   Heidarzade, Armaghan ^a,c   Amiri, Nezam Mahdavi ^d  

^a DEPARTMENT OF INDUSTRIAL ENGINEERING   (Iran)

^b ISLAMIC AZAD UNIVERSITY   (Iran)

^c PAYAME NOOR UNIVERSITY   (Iran)

^d SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Dynamic programming; Fuzzy network; Fuzzy shortest chain

Indexed keywords

FUZZY SETS; GRAPH THEORY; MATLAB; MOTOR TRANSPORTATION; SET THEORY; SYSTEMS ANALYSIS; SYSTEMS ENGINEERING; TRAFFIC CONTROL;

FUZZY NETWORK; FUZZY SHORTEST CHAIN; RANKING METHODS; ROAD NETWORKS; TRAVEL TIME; VEHICLE CAPACITY;

DYNAMIC PROGRAMMING;

EID: 58549099848     PISSN: 15684946     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.asoc.2008.07.002     Document Type: Article

References (29)

1. Bellman R.E., and Zadeh L.A. Decision-making in a fuzzy environment. Management Science 17 (1970) 141-164
2. Blue M., Bush B., and Puckett J. Unified approach to fuzzy graph problems. Fuzzy Sets and Systems 125 (2002) 355-368
3. Bortolan G., and Degani R. A review of some methods for ranking fuzzy subsets. Fuzzy Sets and Systems 15 (1985) 1-19
4. Buckley J.J. The fuzzy mathematics of finance. Fuzzy Sets and Systems 21 (1987) 257-273
5. Chuang T.N., and Kung J.Y. The fuzzy shortest path length and the corresponding shortest path in a network. Computers and Operations Research 32 (2005) 1409-1428
6. Delgado M., Verdegay J.L., and Vila M.A. A procedure for ranking fuzzy numbers using fuzzy relations. Fuzzy Sets and Systems 26 (1988) 49-62
7. Dubois D., and Prade H. Fuzzy Sets and Systems: Theory and Applications (1980), Academic Press, New York
8. Eppstein D. Finding the k-shortest paths. Proc. IEEE Symp. on Foundations of Computer Science (1994)
9. Hansen P., Beckmann M., and Kunzi H.P. Multiple criteria decision making. Theory and Applications, Lecture Note in Economics and in Mathematical Systems, vol. 177 (1980) pp. 109-127
10. Hernandes F., Lemata M.T., Verdegay J.L., and Yamakami A. The shortest path problem on networks with fuzzy parameters. Fuzzy Sets and Systems 158 (2007) 1561-1570
11. Henig M.I. Efficient interactive methods for a class of multi attribute shortest path problems. Management Science 40 (1994) 891-897
12. Jenson P., and Barnes J. Network Flow Programming (1980), John Wiley and Sons, New York
13. Ji X., Iwamura K., and Shao Z. New models for shortest path problem with fuzzy arc lengths. Applied Mathematical Modelling 31 (2007) 259-269
14. Kaufmann A., and Gupta M.M. Introduction to Fuzzy Arithmetic: Theory and Applications (1991), Van Nostrand-Reinhold, New York
15. Klein C.M. Fuzzy shortest paths. Fuzzy Sets and Systems 39 (1991) 27-41
16. Lawler E. Combinational Optimization; Networks and Matroids, Holt (1976), Reinehart and Winston, New York
17. Lin K., and Chen M. The fuzzy shortest path problem and its most vital arcs. Fuzzy Sets and Systems 58 (1994) 343-353
18. Martins E. On a multi criteria shortest path problem. European Journal of Operational Research 16 (1984) 236-245
19. Nayeem S.M.A., and Pal M. Shortest path problem on a network with imprecise edge weight. Fuzzy Optimization Decision Making 4 (2005) 293-312
20. Okada S. Fuzzy shortest path problems incorporating interactivity among paths. Fuzzy Sets and Systems 142 (2004) 335-357
21. Okada S., and Soper T. A Shortest path problem on a network with fuzzy arc lengths. Fuzzy Sets and Systems 109 (2000) 129-140
22. Okada S., and Gen M. Order relation between intervals and its applications to shortest path problem. Proc. 15th Ann. Conf. on Computers and Industrial Engineering 25 (1993)
23. Okada S., and Gen M. Fuzzy shortest path problem. Proc. 16th Ann. Conf. on Computers and Industrial Engineering 27 (1994)
24. Sadeghpour Gildeh, B., Gien, D., La distance-Dp,q et le cofficient de corrélation entre deux variables aléatoires floues, Actes de LFA'2001, 97-102, Monse-Belgium, 2001.
25. Sengupta A., and Pal T.K. On comparing interval numbers. European Journal of Operations Research 127 (2000) 29-43
26. Steebrink P.A. Optimization of Transport Network (1973), John Wiley and Sons
27. Van Vliet D. Improved shortest path algorithms for transport networks. Transportation Research 12 (1978) 7-20
28. Wang X., and Kerre E.E. Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy Sets and Systems 118 (2001) 375-385
29. Zadeh L.A. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1 (1978) 3-28