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Advances in Fuzzy Systems
Volume 2012, Article ID 646248, 6 pages
http://dx.doi.org/10.1155/2012/646248
Research Article

Fuzzy Shortest Path Problem Based on Level 𝜆 -Triangular LR Fuzzy Numbers

Department of Mathematics, Auxilium College (Autonomous), Tamil Nadu, Vellore 632006, India

Received 15 April 2011; Accepted 1 October 2011

Academic Editor: Uzay Kaymak

Copyright © 2012 S. Elizabeth and L. Sujatha. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. A. Zadeh, “Fuzzy sets as a basis for a theory of possibility,” Fuzzy Sets and Systems, vol. 1, no. 1, pp. 3–28, 1978. View at Google Scholar
  2. D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York, NY, USA, 1980.
  3. C. M. Klein, “Fuzzy shortest paths,” Fuzzy Sets and Systems, vol. 39, no. 1, pp. 27–41, 1991. View at Google Scholar
  4. K. C. Lin and M. S. Chern, “The fuzzy shortest path problem and its most vital arcs,” Fuzzy Sets and Systems, vol. 58, no. 3, pp. 343–353, 1993. View at Google Scholar
  5. S. Okada and T. Soper, “A shortest path problem on a network with fuzzy arc lengths,” Fuzzy Sets and Systems, vol. 109, no. 1, pp. 129–140, 2000. View at Google Scholar
  6. T. N. Chuang and J. Y. Kung, “The fuzzy shortest path length and the corresponding shortest path in a network,” Computers and Operations Research, vol. 32, no. 6, pp. 1409–1428, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  7. J. S. Yao and F. T. Lin, “Fuzzy shortest-path network problems with uncertain edge weights,” Journal of Information Science and Engineering, vol. 19, no. 2, pp. 329–351, 2003. View at Google Scholar
  8. S. M. A. Nayeem and M. Pal, “Shortest path problem on a network with imprecise edge weight,” Fuzzy Optimization and Decision Making, vol. 4, no. 4, pp. 293–312, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  9. A. Sengupta and T. K. Pal, “On comparing interval numbers,” European Journal of Operational Research, vol. 127, no. 1, pp. 28–43, 2000. View at Google Scholar
  10. L. Sujatha and R. Sattanathan, “Fuzzy shortest path problem based on triangular LR type fuzzy number using acceptability index,” International Journal of Engineering and Technology, vol. 6, pp. 575–578, 2009. View at Google Scholar
  11. M. Blue, B. Bush, and J. Puckett, “Unified approach to fuzzy graph problems,” Fuzzy Sets and Systems, vol. 125, no. 3, pp. 355–368, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  12. K. P. Sudhir and P. Rimple, Fuzzy Sets and Their Applications, Pragati Prakashan, Meerut, India, 1st edition, 2006.
  13. M. I. Henig, “Efficient interactive methods for a class of multiattribute shortest path problems,” Management Science, vol. 40, no. 7, pp. 891–897, 1994. View at Google Scholar
  14. L. K. Hyung, Y. S. Song, and K. M. Lee, “Similarity measure between fuzzy sets and between elements,” Fuzzy Sets and Systems, vol. 62, no. 3, pp. 291–293, 1994. View at Google Scholar
  15. X. C. Liu, “Entropy, distance measure and similarity measure of fuzzy sets and their relations,” Fuzzy Sets and Systems, vol. 52, no. 3, pp. 305–318, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  16. C. P. Pappis and N. I. Karacapilidis, “A comparative assessment of measures of similarity of fuzzy values,” Fuzzy Sets and Systems, vol. 56, no. 2, pp. 171–174, 1993. View at Google Scholar
  17. J. Ramík and J. Rímánek, “Inequality relation between fuzzy numbers and its use in fuzzy optimization,” Fuzzy Sets and Systems, vol. 16, no. 2, pp. 123–138, 1985. View at Publisher · View at Google Scholar · View at MathSciNet
  18. H. Tanaka, H. Ichihashi, and K. Asai, “A formulation of fuzzy linear programming problem based on comparison of fuzzy numbers,” Control and Cybernetics, vol. 13, pp. 185–194, 1984. View at Google Scholar
  19. W. J. Wang, “New similarity measures on fuzzy sets and on elements,” Fuzzy Sets and Systems, vol. 85, no. 3, pp. 305–309, 1997. View at Google Scholar