Shortest path problem on a network with imprecise edge weight

Fuzzy Optimization and Decision Making

Volumn 4, Issue 4, 2005, Pages 293-312

  Nayeem, Sk Md Abu ^a   Pal, Madhumangal ^a  

^a VIDYASAGAR UNIVERSITY   (India)

Author keywords

Fuzzy; Interval numbers; Network; Shortest path; Triangular fuzzy numbers

Indexed keywords

ALGORITHMS; DECISION MAKING; OPTIMIZATION;

ARC LENGTHS; FUZZY; INTERVAL NUMBERS; NETWORK; SHORTEST PATH; TRIANGULAR FUZZY NUMBERS;

FUZZY SETS;

EID: 26844440728     PISSN: 15684539     EISSN: 15732908     Source Type: Journal    
DOI: 10.1007/s10700-005-3665-2     Document Type: Article

References (21)

1. Blue, M., B. Bush, and J. Puckett. (2002). "Unified approach to Fuzzy Graph Problems," Fuzzy Sets and Systems 125, 355-368.
2. Bortolan, G. and R. Degani. (1985). "A review of some methods for ranking fuzzy subsets," Fuzzy Sets and Systems 15, 1-19.
3. Chen, S.-H. (1985). "Ranking Fuzzy Numbers with Maximizing Set and Minimizing Set," Fuzzy Sets and Systems 17, 113-129.
4. Cheng, C.-H. (1998). "A New Approach for Ranking Fuzzy Numbers by Distance Method," Fuzzy Sets and Systems 95, 307-317.
5. Delgado, M., J. L. Verdegay, and M. A. Vila. (1988). "A Procedure for Ranking Fuzzy Numbers using Fuzzy Relations," Fuzzy Sets and Systems 26, 49-62.
6. Dijkstra, E. W. (1959). "A Note on Two Problems in Connection with Graphs," Numerische Mathematik 1, 269-271.
7. Dubois, D. and H. Prade. (1980). Fuzzy Sets and Systems; Theory and Applications. Academic Press, New York.
8. Dubois, D. and H. Prade. (1983). "Ranking Fuzy Numbers in the Setting of Possiblity Theory," Information Sciences 30, 183-224.
9. Ishibuchi, H. and H. Tanaka. (1990). "Multiobjective Programming in Optimization of The Interval Objective Function," European Journal of Operational Research 48, 219-225.
10. Klein, C. M. (1991). "Fuzzy Shortest Paths," Fuzzy Sets and Systems 39, 27-41.
11. Koczy, L. T. (1992). "Fuzzy Graphs in the Evaluation and Optimization of Networks," Fuzzy Sets and Systems 46, 307-319.
12. Li, Y., M. Gen, and K. Ida. (1996). "Solving Fuzzy Shortest Path Problem by Neural Networks," Comput. Ind. Eng. 31, 861-865.
13. Lin, K. and M. Chen. (1994). "The Fuzzy Shortest Path Problem and its Most Vital Arcs," Fuzzy Sets and Systems 58, 343-353.
14. Moore, R. E. (1997). Method and Application of Interval Analysis, SIAM, Philadelphia.
15. Okada, S. and M. Gen. (1993). "Order Relation Between Intervals and its Application to Shortest Path Problem," Comput. Ind. Eng. 25, 147-150.
16. Okada, S. and M. Gen. (1994). "Fuzzy Shortest Path Problem," Comput. Ind. Eng. 27, 465-468.
17. Okada, S. and T. Soper. (2000). "A Shortest Path Problem on a Network with Fuzzy Arc Lengths," Fuzzy Sets and Systems 109, 129-140.
18. Sengupta, A. and T. K. Pal. (2000). "Theory and Methodology on Comparing Interval Numbers," European Journal of Operational Research 127, 28-43.
19. Sengupta, J. K. (1981). Optimal Decision under Uncertainty, Springer, New York.
20. Shaocheng, T. (1994). "Interval Number and Fuzzy Number Linear Programmings," Fuzzy Sets and Systems 66, 301-306.
21. SPLIB (http://www.avglab.com/andrew/soft.html)