Deviation Square Priority Method for Distinct Preference Structures Based on Generalized Multiplicative Consistency

IEEE Transactions on Fuzzy Systems

Volumn 23, Issue 4, 2015, Pages 1164-1180

  Xu, Zeshui ^a  

^a Department of Management Science and System Science   (China)

Author keywords

Group decision making; iterative algorithm; multiplicative consistency; nonlinear optimization model; preference relation

Indexed keywords

ALGORITHMS; DIESEL ENGINES; FUZZY SET THEORY; ITERATIVE METHODS; MACHINE DESIGN; NONLINEAR EQUATIONS; NONLINEAR PROGRAMMING; OPTIMIZATION;

GROUP DECISION MAKING; ITERATIVE ALGORITHM; MULTIPLICATIVE CONSISTENCY; NONLINEAR OPTIMIZATION MODEL; PREFERENCE RELATION;

DECISION MAKING;

EID: 84938787434     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2014.2346794     Document Type: Article

References (29)

1. S.A.Orlovsky, "Decision-making with a fuzzy preference relation," Fuzzy Sets Syst., vol. 1, pp. 155-167, 1978.
2. J. C. Bezdek, B. Spillman, and R. Spillman, "A fuzzy relation space for group decision theory," Fuzzy Sets Syst., vol. 1, pp. 255-268, 1978.
3. Z. S. Xu, "Goal programming models for obtaining the priority vector of incomplete fuzzy preference relation," Int. J. Approx. Reason., vol. 36, pp. 261-270, 2004.
4. R. D. Luce and P. Suppes, "Preferences, utility and subject probability," in Handbook of Mathematical Psychology, vol. 3, R. D. Luce, R. Bush, and E. Galanter, Eds. New York, NY, USA: Wiley, 1965, pp. 249-410,.
5. A. K. Sen, Collective Choice and Social Welfare. San Francisco, CA, USA: Holden-Day, 1970.
6. T. Tanino, "Fuzzy preference orderings in group decision making," Fuzzy Sets Syst., vol. 12, pp. 117-131, 1984.
7. H. Nurmi, "Approaches to collective decision making with fuzzy preference relations," Fuzzy Sets Syst., vol. 6, pp. 249-259, 1981.
8. S. Lipovetsky and W. Michael Conklin, "Robust estimation of priorities in the AHP," Eur. J. Oper. Res., vol. 137, pp. 110-122, 2002.
9. Z. S. Xu and Q. L. Da, "A least deviationmethod to obtain a priority vector of a fuzzy preference relation," Eur. J. Oper. Res., vol. 164, pp. 206-216, 2005.
10. E. Herrera-Viedma, F. Herrera, F. Chiclana, and M. Luque, "Some issues on consistency of fuzzy preference relations," Eur. J. Oper. Res., vol. 154, pp. 98-109, 2004.
11. Z. S. Xu, "A survey of preference relations," Int. J. Gen. Syst., vol. 36, pp. 179-203, 2007.
12. T. Tanino, "Fuzzy preference relations in group decision making," in Non- Conventional Preference Relations in Decision Making, J. Kacprzyk and M. Roubens, Eds. Berlin, Germany: Springer-Verlag, 1988, pp. 54-71.
13. Y. M. Wang and Z. P. Fan, "Group decision analysis based on fuzzy preference relations: Logarithmic and geometric least squares methods," Appl. Math. Comput., vol. 194, pp. 108-119, 2007.
14. Y. M.Wang, Z. P. Fan, and Z. S. Hua, "A chi-square method for obtaining a priority vector from multiplicative and fuzzy preference relations," Eur. J. Oper. Res., vol. 182, pp. 356-366, 2007.
15. F. Herrera, E. Herrera-Viedma, and F. Chiclana, "Multiperson decisionmaking based on multiplicative preference relations," Eur. J. Oper. Res., vol. 129, pp. 372-385, 2001.
16. J. Ma, Z. P. Fan, Y. P. Jiang, and J. Y. Mao, "An optimization approach to multiperson decision making based on different formats of preference information," IEEE Trans. Syst., Man, Cybern. A, Syst., Humans, vol. 36, no. 5, pp. 876-889, Sep. 2006.
17. Z. S. Xu, "A procedure for decision making based on incomplete fuzzy preference relation," Fuzzy Optim. Decision Making, vol. 4, pp. 175-189, 2005.
18. Z. S. Xu, X. Q. Cai, and S. S. Liu, "Nonlinear programming model integrating different preference structures," IEEE Trans. Syst., Man, Cybern. A, Syst., Humans, vol. 41, no. 1, pp. 169-177, Jan. 2011.
19. M. Fedrizzi and M. Brunelli, "On the normalisation of a priority vector associated with a reciprocal relation," Int. J. Gen. Syst., vol. 38, pp. 579-586, 2009.
20. F. Chiclana, F. Herrera, and E. Herrera-Viedma, "Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations," Fuzzy Sets Syst., vol. 97, pp. 33-48, 1998.
21. S. E. Bodily, "A delegation process for combining individual utility functions," Manage. Sci., vol. 25, pp. 1035-1041, 1979.
22. H. W. Brock, "The problem of utility weights in group preference aggregation," Oper. Res., vol. 28, pp. 176-187, 1980.
23. R. Ramanathan and L. S. Ganesh, "Group preference aggregation methods employed in AHP: An evaluation and an intrinsic process for deriving members' weightages," Eur. J. Oper. Res., vol. 79, pp. 249-265, 1994.
24. J. Kacprzyk, "Group decision making with a fuzzy linguistic majority," Fuzzy Sets Syst., vol. 18, pp. 105-118, 1986.
25. Z. S. Xu and J. Chen, "Group decision-making procedure based on incomplete reciprocal relations," Soft Comput., vol. 12, pp. 515-521, 2008.
26. N. C. Surawski, B. Miljevic, T. A. Bodisco, R. J. Brown, Z. D. Ristovski, and G. A. Ayoko, "Application of multicriteria decision making methods to compression ignition engine efficiency and gaseous, particulate, and greenhouse gas emissions," Environ. Sci. Technol., vol. 47, pp. 1904-1912, 2013.
27. E. Herrera-Viedma, S. Alonso, F. Chiclana, and F. Herrera, "A consensus model for group decision making with incomplete fuzzy preference relations," IEEE Trans. Fuzzy Syst., vol. 15, no. 5, pp. 863-877, Oct. 2007.
28. T. L. Saaty, "A scaling method for priorities in hierarchical structures," J. Math. Psychol., vol. 15, pp. 234-281, 1977.
29. H. Bustince, M. Pagola, R. Mesiar, E.Hullermeier, and F. Herrera, "Grouping, overlap and generalized bi-entropic functions for fuzzy modeling of pairwise comparisons," IEEE Trans. Fuzzy Syst., vol. 20, no. 3, pp. 405-415, Jun. 2012.