- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Applied Computational Intelligence and Soft Computing
Volume 2013 (2013), Article ID 970197, 5 pages
An Algorithm for Extracting Intuitionistic Fuzzy Shortest Path in a Graph
Department of Computer Engineering, Faculty of Engineering & Technology, Jamia Millia Islamia, New Delhi 110025, India
Received 15 September 2013; Accepted 5 October 2013
Academic Editor: Baoding Liu
Copyright © 2013 Siddhartha Sankar Biswas et al. 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.
- V. K. Balakrishnan, Graph Theory, McGraw-Hill, New York, NY, USA, 1997.
- B. Bollobas, Modern Graph Theory, Springer, New York, NY, USA, 2002.
- R. Diestel, Graph Theory, Springer, 2000.
- F. Harary, Graph Theory, Addison Wesley, Boston, Mass, USA, 1995.
- D. Dubois and H. Prade, Fuzzy Sets and Systems, Academic Press, New York, NY, USA, 1980.
- C. M. Klein, “Fuzzy shortest paths,” Fuzzy Sets and Systems, vol. 39, no. 1, pp. 27–41, 1991.
- 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.
- L. Sujatha and S. Elizabeth, “Fuzzy shortest path problem based on similarity degree,” Applied Mathematical Sciences, vol. 5, no. 66, pp. 3263–3276, 2011.
- 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.
- J.-R. Yu and T.-H. Wei, “Solving the fuzzy shortest path problem by using a linear multiple objective programming,” Journal of the Chinese Institute of Industrial Engineers, vol. 24, no. 5, pp. 360–365, 2007.
- S. Mukherjee, “Dijkstra’s algorithm for solving the shortest path problem on networks under intuitionistic fuzzy environment,” Journal of Mathematical Modelling and Algorithms, vol. 11, no. 4, pp. 345–359, 2012.
- M. G. Karunambigai, P. Rangasamy, K. Atanassov, and N. Palaniappan, “An intuitionistic fuzzy graph method for finding the shortest paths in networks,” Advances in Soft Computing, vol. 42, pp. 3–10, 2007.
- A. Nagoor Gani and M. Mohammed Jabarulla, “On searching intuitionistic fuzzy shortest path in a network,” Applied Mathematical Sciences, vol. 4, no. 69, pp. 3447–3454, 2010.
- K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87–96, 1986.
- K. Atanassov, Intuitionistic Fuzzy Sets:Theory and Applications, Physica, 1999.
- K. T. Atanassov, “More on intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 33, no. 1, pp. 37–45, 1989.
- D.-F. Li, “A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems,” Computers and Mathematics with Applications, vol. 60, no. 6, pp. 1557–1570, 2010.
- D. F. Li, J. X. Nan, and M. J. Zhang, “A ranking method of triangular intuitionistic fuzzy numbers and application to decision making,” International Journal of Computational Intelligence Systems, vol. 3, no. 5, pp. 522–530, 2010.
- H. B. Mitchell, “Ranking-intuitionistic fuzzy numbers,” International Journal of Uncertainty, Fuzziness and Knowlege-Based Systems, vol. 12, no. 3, pp. 377–386, 2004.
- S. Abbasbandy, “Ranking of fuzzy numbers, some recent and new formulas,” in Proceedings of the IFSA-EUSFLAT, pp. 642–646, Lisbon, Portugal, July 2009.
- T. Allahviranloo, S. Abbasbandy, and R. Saneifard, “A method for ranking of fuzzy numbers using new weighted distance,” Mathematical and Computational Applications, vol. 16, no. 2, pp. 359–369, 2011.
- L. Q. Dat, V. F. Yu, and S. Y. Chou, “An improved ranking method for fuzzy numbers using left and right indices,” in Proceedings of the 2nd International Conference on Computer Design and Engineering (IPCSIT '12), vol. 49, pp. 89–94, 2012.
- B. Farhadinia, “Ranking fuzzy numbers on lexicographical ordering,” International Journal of Applied Mathematics and Computer Sciences, vol. 5, no. 4, pp. 248–251, 2009.
- N. Parandin, Araghi, and M. A. Fariborzi, “Ranking of fuzzy numbers by distance method,” Journal of Applied Mathematics, vol. 5, no. 19, pp. 47–55, 2008.
- N. R. Shankar and P. P. B. Rao, “Ranking fuzzy numbers with a distance method using circumcenter of centroids and an index of modality,” Advances in Fuzzy Systems, vol. 2011, Article ID 178308, 7 pages, 2011.
- R. Saneifard and R. Ezzati, “A new approach for ranking fuzzy numbers with continuous weighted quasi-arithmatic means,” Mathematical Sciences, vol. 4, no. 2, pp. 143–158, 2010.
- R. Biswas, “Fuzzy numbers redefined,” Information, vol. 15, no. 4, pp. 1369–1380, 2012.