Table of Contents Author Guidelines Submit a Manuscript
Advances in Operations Research
Volume 2012 (2012), Article ID 574710, 17 pages
http://dx.doi.org/10.1155/2012/574710
Research Article

Deriving Weights of Criteria from Inconsistent Fuzzy Comparison Matrices by Using the Nearest Weighted Interval Approximation

Department of Mathematics, Islamic Azad University, Arak-Branch, Arak, Iran

Received 2 March 2012; Accepted 25 April 2012

Academic Editor: Yi Kuei Lin

Copyright © 2012 Mohammad Izadikhah. 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. O. S. Vaidya and S. Kumar, “Analytic hierarchy process: an overview of applications,” European Journal of Operational Research, vol. 169, no. 1, pp. 1–29, 2006. View at Publisher · View at Google Scholar · View at Scopus
  2. Z. S. Xu and Q. L. Da, “The uncertain OWA operator,” International Journal of Intelligent Systems, vol. 17, no. 6, pp. 569–575, 2002. View at Publisher · View at Google Scholar · View at Scopus
  3. Z. P. Fan, J. Ma, and Q. Zhang, “An approach to multiple attribute decision making based on fuzzy preference information on alternatives,” Fuzzy Sets and Systems, vol. 131, no. 1, pp. 101–106, 2002. View at Publisher · View at Google Scholar · View at Scopus
  4. Z. S. Xu and Q. L. Da, “An approach to improving consistency of fuzzy preference matrix,” Fuzzy Optimization and Decision Making, vol. 2, no. 1, pp. 3–12, 2003. View at Publisher · View at Google Scholar · View at Scopus
  5. Z. S. Xu and Q. L. Da, “A least deviation method to obtain a priority vector of a fuzzy preference relation,” European Journal of Operational Research, vol. 164, no. 1, pp. 206–216, 2005. View at Publisher · View at Google Scholar · View at Scopus
  6. A. M. Geoffrion, J. S. Dyer, and A. Feinberg, “An interactive approach for multicriterion optimization with an application to operation of an academic department,” Management Science, vol. 19, no. 4, pp. 357–368, 1972. View at Google Scholar · View at Scopus
  7. Y. Y. Haimes, “The surrogate worth trade-off (SWT) method and its extensions,” in Multiple Criteria Decision Making Theory and Application, G. Fandel and T. Gal, Eds., New York, NY, USA, Springer, 1980. View at Google Scholar
  8. S. Zionts and K. Wallenius, “An interactive programming method for solving the multiple criteria problem,” Management Science, vol. 22, no. 6, pp. 652–663, 1976. View at Google Scholar · View at Scopus
  9. T. L. Saaty, The Analytic Hierarchy Process, McGraw-Hill, New York, NY, USA, 1980.
  10. K. O. Cogger and P. L. Yu, “Eigenweight vectors and least-distance approximation for revealed preference in pairwise weight ratios,” Journal of Optimization Theory and Applications, vol. 46, no. 4, pp. 483–491, 1985. View at Publisher · View at Google Scholar · View at Scopus
  11. E. Takeda, K. O. Cogger, and P. L. Yu, “Estimating criterion weights using eigenvectors: a comparative study,” European Journal of Operational Research, vol. 29, no. 3, pp. 360–369, 1987. View at Google Scholar · View at Scopus
  12. L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338–353, 1965. View at Google Scholar · View at Scopus
  13. R. E. Bellman and L. A. Zadeh, “Decision making in a fuzzy environment,” Management Science, vol. 17, no. 4, pp. 141–164, 1970. View at Google Scholar · View at Scopus
  14. R. Islam, M. P. Biswal, and S. S. Alam, “Preference programming and inconsistent interval judgments,” European Journal of Operational Research, vol. 97, no. 1, pp. 53–62, 1997. View at Google Scholar · View at Scopus
  15. Y. M. Wang, “On lexicographic goal programming method for generating weights from inconsistent interval comparison matrices,” Applied Mathematics and Computation, vol. 173, no. 2, pp. 985–991, 2006. View at Publisher · View at Google Scholar · View at Scopus
  16. Y.-M. Wang and K.-S. Chin, “An eigenvector method for generating normalized interval and fuzzy weights,” Applied Mathematics and Computation, vol. 181, no. 2, pp. 1257–1275, 2006. View at Publisher · View at Google Scholar · View at Scopus
  17. Z. Xu and J. Chen, “Some models for deriving the priority weights from interval fuzzy preference relations,” European Journal of Operational Research, vol. 184, no. 1, pp. 266–280, 2008. View at Publisher · View at Google Scholar · View at Scopus
  18. Y. M. Wang and K. S. Chin, “A linear goal programming priority method for fuzzy analytic hierarchy process and its applications in new product screening,” International Journal of Approximate Reasoning, vol. 49, no. 2, pp. 451–465, 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. Z. Taha and S. Rostam, “A fuzzy AHP-ANN-based decision support system for machine tool selection in a flexible manufacturing cell,” International Journal of Advanced Manufacturing Technology, vol. 57, no. 5–8, pp. 719–733, 2011. View at Publisher · View at Google Scholar · View at Scopus
  20. Z. Ayaǧ and R. G. Özdemir, “A hybrid approach to concept selection through fuzzy analytic network process,” Computers and Industrial Engineering, vol. 56, no. 1, pp. 368–379, 2009. View at Publisher · View at Google Scholar · View at Scopus
  21. J. Barzilai, “Deriving weights from pairwise comparison matrices,” Journal of the Operational Research Society, vol. 48, no. 12, pp. 1226–1232, 1997. View at Google Scholar · View at Scopus
  22. A. Salo and R. Haimalainen, “On the measurement of preferences in the analytic hierarchy process,” Journal of Multi-Criteria Decision Analysis, vol. 6, pp. 309–319, 1997. View at Google Scholar
  23. A. Saeidifar, “Application of weighting functions to the ranking of fuzzy numbers,” Computers and Mathematics with Applications, vol. 62, pp. 2246–2258, 2011. View at Publisher · View at Google Scholar · View at Scopus
  24. A. Charnes and W. W. Cooper, Management Model and Industrial Application of Linear Programming, vol. 1, Wiley, New York, NY, USA, 1961.
  25. B. Asady and A. Zendehnam, “Ranking fuzzy numbers by distance minimization,” Applied Mathematical Modelling, vol. 31, no. 11, pp. 2589–2598, 2007. View at Publisher · View at Google Scholar · View at Scopus
  26. S. J. Chen, C. L. Hwang, and E. P. Hwang, “Fuzzy multiple attribute decision making,” in Lecture Notes in Economics and Mathematical Systems, vol. 375, Springer, Berlin, Germany, 1992. View at Google Scholar
  27. J. Ramík and P. Korviny, “Inconsistency of pair-wise comparison matrix with fuzzy elements based on geometric mean,” Fuzzy Sets and Systems, vol. 161, no. 11, pp. 1604–1613, 2010. View at Publisher · View at Google Scholar · View at Scopus