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The Scientific World Journal
Volume 2013, Article ID 202085, 8 pages
http://dx.doi.org/10.1155/2013/202085
Research Article

A Method to Dynamic Stochastic Multicriteria Decision Making with Log-Normally Distributed Random Variables

1School of Science, Hunan University of Technology, Zhuzhou 412007, China
2School of Business, Central South University, Changsha 410083, China

Received 4 August 2013; Accepted 22 August 2013

Academic Editors: A. Amirteimoori and S. W. Chiu

Copyright © 2013 Xin-Fan Wang 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.

Linked References

  1. R. Lahdelma, S. Makkonen, and P. Salminen, “Multivariate Gaussian criteria in SMAA,” European Journal of Operational Research, vol. 170, no. 3, pp. 957–970, 2006. View at Publisher · View at Google Scholar · View at Scopus
  2. S. Yao and C. Yue, “Approach to stochastic multi-attribute decision problems using rough sets theory,” Journal of Systems Engineering and Electronics, vol. 17, no. 1, pp. 103–108, 2006. View at Publisher · View at Google Scholar · View at Scopus
  3. G.-T. Jiang, Z.-P. Fan, and Y. Liu, “Method for multiple attribute decision making with normal random variables,” Control and Decision, vol. 24, no. 8, pp. 1187–1197, 2009. View at Google Scholar · View at Scopus
  4. Y. Liu, Z.-P. Fan, and Y. Zhang, “A method for normal stochastic multiple attribute decision making considering interactions among attributes,” Operations Research and Mangement Science, vol. 20, no. 5, pp. 20–26, 2011. View at Google Scholar
  5. G. T. Jiang and Z.-P. Fan, “A method for MADM with normal random variables,” Systems Engineering—Theory & Practice, vol. 32, no. 7, pp. 1517–1524, 2012. View at Google Scholar
  6. J.-Q. Wang and J. Ren, “Stochastic multi-criteria decision-making method based on WC-OWA operator,” Control and Decision, vol. 22, no. 12, pp. 1429–1432, 2007. View at Google Scholar · View at Scopus
  7. J. Ren and Y. Gao, “Stochastic multi-criterion decision-making method based on interval operation,” Systems Engineering and Electronics, vol. 32, no. 2, pp. 308–312, 2010. View at Google Scholar · View at Scopus
  8. X.-F. Wang and X.-J. Yang, “Dynamic stochastic multiple attribute decision making method with incomplete certain information,” System Engineering —Theory& Practice, vol. 30, no. 2, pp. 332–338, 2010. View at Google Scholar · View at Scopus
  9. X. Zhang and Z.-P. Fan, “Method for stochastic multiple attribute decision making based on prospect stochastic dominance rule,” Control and Decision, vol. 25, no. 12, pp. 1875–1879, 2010. View at Google Scholar · View at Scopus
  10. K. Zaras, “Rough approximation of a preference relation by a multi-attribute stochastic dominance for determinist and stochastic evaluation problems,” European Journal of Operational Research, vol. 130, no. 2, pp. 305–314, 2001. View at Publisher · View at Google Scholar · View at Scopus
  11. M. Kadziński and T. Tervonen, “Stochastic ordinal regression for multiple criteria sorting problems,” Decision Support Systems, vol. 55, no. 1, pp. 55–66, 2013. View at Publisher · View at Google Scholar
  12. Z.-P. Fan, Y. Liu, and B. Feng, “A method for stochastic multiple criteria decision making based on pairwise comparisons of alternatives with random evaluations,” European Journal of Operational Research, vol. 207, no. 2, pp. 906–915, 2010. View at Publisher · View at Google Scholar · View at Scopus
  13. Y. Liu, Z.-P. Fan, and Y. Zhang, “A method for stochastic multiple criteria decision making based on dominance degrees,” Information Sciences, vol. 181, no. 19, pp. 4139–4153, 2011. View at Publisher · View at Google Scholar · View at Scopus
  14. M. Nowak, “Aspiration level approach in stochastic MCDM problems,” European Journal of Operational Research, vol. 177, no. 3, pp. 1626–1640, 2007. View at Publisher · View at Google Scholar · View at Scopus
  15. K. Zaras, “Rough approximation of a preference relation by a multi-attribute dominance for deterministic, stochastic and fuzzy decision problems,” European Journal of Operational Research, vol. 159, no. 1, pp. 196–206, 2004. View at Publisher · View at Google Scholar · View at Scopus
  16. J. Aitchison and J. A. C. Brown, The Lognormal Distribution, Cambridge University Press, Cambridge, UK, 1957.
  17. E. L. Crow and K. Shimizu, Lognormal Distributions: Theory and Application, Dekker, New York, NY, USA, 1988.
  18. E. Limpert, W. A. Stahel, and M. Abbt, “Log-normal distributions across the sciences: keys and clues,” BioScience, vol. 51, no. 5, pp. 341–352, 2001. View at Google Scholar · View at Scopus
  19. I. Antoniou, V. V. Ivanov, V. V. Ivanov, and P. V. Zrelov, “On the log-normal distribution of stock market data,” Physica A, vol. 331, no. 3-4, pp. 617–638, 2004. View at Publisher · View at Google Scholar · View at Scopus
  20. R. C. Merton and P. A. Samuelson, “Fallacy of the log-normal approximation to optimal portfolio decision-making over many periods,” Journal of Financial Economics, vol. 1, no. 1, pp. 67–94, 1974. View at Google Scholar · View at Scopus
  21. L. W. Chen, Project Investment Risk Analysis: Theories and Methods, China Machine Press, Beijing, China, 2004.
  22. G. McPherson, Statistics in Scientific Investigation: Its Basis, Application and Interpretation, Springer, New York, NY, USA, 1990.
  23. J. C. Harsanyi, “Cardinal welfare, individualistic ethics, and interpersonal comparisions of utility,” Journal of Political Economy, vol. 63, no. 4, pp. 309–321, 1955. View at Publisher · View at Google Scholar
  24. Z. Xu, “On multi-period multi-attribute decision making,” Knowledge-Based Systems, vol. 21, no. 2, pp. 164–171, 2008. View at Publisher · View at Google Scholar · View at Scopus
  25. Z. Xu and R. R. Yager, “Dynamic intuitionistic fuzzy multi-attribute decision making,” International Journal of Approximate Reasoning, vol. 48, no. 1, pp. 246–262, 2008. View at Publisher · View at Google Scholar · View at Scopus
  26. R. Sadiq and S. Tesfamariam, “Probability density functions based weights for ordered weighted averaging (OWA) operators: an example of water quality indices,” European Journal of Operational Research, vol. 182, no. 3, pp. 1350–1368, 2007. View at Publisher · View at Google Scholar · View at Scopus
  27. Z. Xu, “Approaches to multi-stage multi-attribute group decision making,” International Journal of Information Technology and Decision Making, vol. 10, no. 1, pp. 121–146, 2011. View at Publisher · View at Google Scholar · View at Scopus
  28. Z. S. Xu and J. Chen, “Binomial distribution based approach to deriving time series weights,” in Proceedings of the IEEE International Conference on Industrial Engineering and Engineering Management (IEEM '07), pp. 154–158, Singapore, December 2007. View at Publisher · View at Google Scholar · View at Scopus
  29. Y.-J. Guo, Y. Yao, and P.-T. Yi, “Method and application of dynamic comprehensive evaluation,” System Engineering —Theory& Practice, vol. 27, no. 10, pp. 154–158, 2007. View at Google Scholar · View at Scopus
  30. R. R. Yager, “On ordered weighted averaging aggregation operators in multicriteria decision making,” IEEE Transactions on Systems, Man and Cybernetics, vol. 18, no. 1, pp. 183–190, 1988. View at Publisher · View at Google Scholar · View at Scopus
  31. R. R. Yager, “Time series smoothing and OWA aggregation,” IEEE Transactions on Fuzzy Systems, vol. 16, no. 4, pp. 994–1007, 2008. View at Publisher · View at Google Scholar · View at Scopus