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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 657978, 9 pages
http://dx.doi.org/10.1155/2013/657978
Research Article

Fuzzy Group Decision Making for Multiobjective Problems: Tradeoff between Consensus and Robustness

1Department of Management, College of Information System and Management, National University of Defense Technology, Changsha, Hunan 410073, China
2School of Software, Shenzhen Institute of Information Technology, Shenzhen 518172, China

Received 3 April 2013; Revised 24 June 2013; Accepted 12 July 2013

Academic Editor: Jianming Zhan

Copyright © 2013 Jian Xiong 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. U. Bose, A. M. Davey, and D. L. Olson, “Multi-attribute utility methods in group decision making: past applications and potential for inclusion in GDSS,” Omega, vol. 25, no. 6, pp. 691–706, 1997. View at Scopus
  2. J. Lu, G. Zhang, D. Ruan, and F. Wu, Multi-Objective Group Decision Making: Methods, Software and Applications with Fuzzy Set Technology, Imperial College Press, London, UK, 2007.
  3. G. Zhang, J. Ma, and J. Lu, “Emergency management evaluation by a fuzzy multi-criteria group decision support system,” Stochastic Environmental Research and Risk Assessment, vol. 23, no. 4, pp. 517–527, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. L. Thiele, K. Miettinen, P. J. Korhonen, and J. Molina, “A preference-based evolutionary algorithm for multi-objective optimization,” Evolutionary Computation, vol. 17, no. 3, pp. 411–436, 2009. View at Publisher · View at Google Scholar · View at Scopus
  5. H. A. Abbass, “An inexpensive cognitive approach for bi-objective optimization using bliss points and interaction,” in Proceedings of the 8th International Conference on Parallel Problem Solving From Nature (PPSN), vol. 3242 of Lecture Notes in Computer Science, pp. 712–721, Springer, New York, NY, USA, 2004.
  6. H. A. Abbass, “An economical cognitive approach for bi-objective optimization using bliss points, visualization, and interaction,” Soft Computing, vol. 10, no. 8, pp. 687–698, 2006. View at Publisher · View at Google Scholar · View at Scopus
  7. H. A. Abbass and A. Bender, “The Pareto operating curve for risk minimization in life and robotics,” Artificial Life Robotics, vol. 14, no. 4, pp. 449–452, 2009. View at Publisher · View at Google Scholar
  8. L. T. Bui, H. A. Abbass, M. Barlow, and A. Bender, “Robustness against the decision-maker's attitude to risk in problems with conflicting objectives,” IEEE Transactions on Evolutionary Computation, vol. 16, no. 1, pp. 1–19, 2012. View at Publisher · View at Google Scholar · View at Scopus
  9. Y. Y. Haimes, Risk Modeling, Assessment, and Management, John Wiley & Sons, Hoboken, NJ, USA, 3rd edition, 2008. View at MathSciNet
  10. M. Ehrgott and X. Gandibleux, “Approximative solution methods for multiobjective combinatorial optimization,” Top, vol. 12, no. 1, pp. 1–63, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. C. A. C. Coello, “Evolutionary multi-objective optimization: a historical view of the field,” IEEE Computational Intelligence Magazine, vol. 1, no. 1, pp. 28–36, 2006. View at Publisher · View at Google Scholar · View at Scopus
  12. E. Zitzler and L. Thiele, “Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach,” IEEE Transactions on Evolutionary Computation, vol. 3, no. 4, pp. 257–271, 1999. View at Publisher · View at Google Scholar · View at Scopus
  13. E. Zitzler, M. Laumanns, and L. Thiele, “Spea2: Improving the strenth Pareto evolutionary algorithm,” in Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems (EUROGEN 2001), K. Giannakoglou, Ed., pp. 95–100, International Center for Numerical Methods in Engineering, Athens, Greece, 2002.
  14. J. D. Knowles and D. W. Corne, “Approximating the nondominated front using the Pareto archived evolution strategy,” Evolutionary Computation, vol. 8, no. 2, pp. 149–172, 2000. View at Scopus
  15. K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182–197, 2002. View at Publisher · View at Google Scholar · View at Scopus
  16. S. Phelps and M. Köksalan, “An interactive evolutionary metaheuristic for multiobjective combinatorial optimization,” Management Science, vol. 49, no. 12, pp. 1726–1738, 2003. View at Scopus
  17. K. Deb and J. Sundar, “Reference point based multi-objective optimization using evolutionary algorithms,” in Proceedings of the 8th Annual Genetic and Evolutionary Computation Conference (GECCO '06), pp. 635–642, Seattle, Wash, USA, July 2006. View at Scopus
  18. K. Deb and S. Chaudhuri, “I-MODE: an interactive multi-objective optimization and decision-making using evolutionary methods,” in Evolutionary Multi-Criterion Optimization, S. Obayashi, Ed., vol. 4403 of Lecture Notes in Computer Science, pp. 788–802, Springer, Berlin, Germany, 2007.
  19. J. Hakanen, Y. Kawajiri, K. Miettinen, and L. T. Biegler, “Interactive multi-objective optimization for simulated moving bed processes,” Control and Cybernetics, vol. 36, no. 2, pp. 283–302, 2007. View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  20. S. Chaudhuri and K. Deb, “An interactive evolutionary multi-objective optimization and decision making procedure,” Applied Soft Computing Journal, vol. 10, no. 2, pp. 496–511, 2010. View at Publisher · View at Google Scholar · View at Scopus
  21. J. Xiong, K. W. Yang, J. Liu, Q. S. Zhao, and Y. W. Chen, “A two-stage preference-based evolutionary multi-objective approach for capability planning problems,” Knowledge-Based Systems, vol. 31, pp. 128–139, 2012. View at Publisher · View at Google Scholar · View at Scopus
  22. J. Lu, G. Zhang, and D. Ruan, “Intelligent multi-criteria fuzzy group decision-making for situation assessments,” Soft Computing, vol. 12, no. 3, pp. 289–299, 2008. View at Publisher · View at Google Scholar · View at Scopus
  23. R. A. Krohling and V. C. Campanharo, “Fuzzy TOPSIS for group decision making: a case study for accidents with oil spill in the sea,” Expert Systems with Applications, vol. 38, no. 4, pp. 4190–4197, 2011. View at Publisher · View at Google Scholar · View at Scopus
  24. J. Lu, J. Ma, G. Zhang, Y. Zhu, X. Zeng, and L. Koehl, “Theme-based comprehensive evaluation in new product development using fuzzy hierarchical criteria group decision-making method,” IEEE Transactions on Industrial Electronics, vol. 58, no. 6, pp. 2236–2246, 2011. View at Publisher · View at Google Scholar · View at Scopus
  25. J. Xiong, Y. Chen, K. Yang, and J. Liu, “A decision support model for multi-attribute group decision making using a multi-objective optimization approach,” International Journal of Computational Intelligence Systems, vol. 6, no. 2, pp. 337–353, 2013. View at Publisher · View at Google Scholar
  26. J. Ma, J. Lu, and G. Zhang, “Decider: a fuzzy multi-criteria group decision support system,” Knowledge-Based Systems, vol. 23, no. 1, pp. 23–31, 2010. View at Publisher · View at Google Scholar · View at Scopus
  27. J. Kacprzyk, M. Fedrizzi, and H. Nurmi, “Group decision making and consensus under fuzzy preferences and fuzzy majority,” Fuzzy Sets and Systems, vol. 49, no. 1, pp. 21–31, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  28. F. Herrera, E. Herrera-Viedma, and J. L. Verdegay, “A model of consensus in group decision making under linguistic assessments,” Fuzzy Sets and Systems, vol. 78, no. 1, pp. 73–87, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. E. Herrera-Viedma, F. Herrera, and F. Chiclana, “A consensus model for multiperson decision making with different preference structures,” IEEE Transactions on Systems, Man, and Cybernetics A, vol. 32, no. 3, pp. 394–402, 2002. View at Publisher · View at Google Scholar · View at Scopus
  30. S. Alonso, E. Herrera-Viedma, F. Chiclana, and F. Herrera, “A web based consensus support system for group decision making problems and incomplete preferences,” Information Sciences, vol. 180, no. 23, pp. 4477–4495, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  31. F. J. Cabrerizo, J. M. Moreno, I. J. Pérez, and E. Herrera-Viedma, “Analyzing consensus approaches in fuzzy group decision making: advantages and drawbacks,” Soft Computing, vol. 14, no. 5, pp. 451–463, 2010. View at Publisher · View at Google Scholar · View at Scopus
  32. H. M. Hsu and C. T. Chen, “Aggregation of fuzzy opinions under group decision making,” Fuzzy Sets and Systems, vol. 79, no. 3, pp. 279–285, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  33. F. Herrera, E. Herrera-Viedma, and J. L. Verdegay, “Linguistic measures based on fuzzy coincidence for reaching consensus in group decision making,” International Journal of Approximate Reasoning, vol. 16, no. 3-4, pp. 309–334, 1997. View at Scopus
  34. E. Herrera-Viedma, L. Martínez, F. Mata, and F. Chiclana, “A consensus support system model for group decision-making problems with multigranular linguistic preference relations,” IEEE Transactions on Fuzzy Systems, vol. 13, no. 5, pp. 644–658, 2005. View at Publisher · View at Google Scholar · View at Scopus
  35. F. Mata, L. Martínez, and E. Herrera-Viedma, “An adaptive consensus support model for group decision-making problems in a multigranular fuzzy linguistic context,” IEEE Transactions on Fuzzy Systems, vol. 17, no. 2, pp. 279–290, 2009. View at Publisher · View at Google Scholar · View at Scopus
  36. Z. Xu, “An automatic approach to reaching consensus in multiple attribute group decision making,” Computers and Industrial Engineering, vol. 56, no. 4, pp. 1369–1374, 2009. View at Publisher · View at Google Scholar · View at Scopus
  37. Z. Wu and J. Xu, “A consistency and consensus based decision support model for group decision making with multiplicative preference relations,” Decision Support Systems, vol. 52, no. 3, pp. 757–767, 2012. View at Publisher · View at Google Scholar · View at Scopus
  38. L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338–353, 1965. View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  39. C. T. Chen, “Extensions of the TOPSIS for group decision-making under fuzzy environment,” Fuzzy Sets and Systems, vol. 114, no. 1, pp. 1–9, 2000. View at Scopus
  40. T. T. Binh and U. Korn, “An evolution strategy for the multiobjective optimization,” in Proceedings of the 2nd International Conference on Genetic Algorithms, pp. 23–28, 1996.