Eigenvector method, consistency test and inconsistency repairing for an incomplete fuzzy preference relation

Applied Mathematical Modelling

Volumn 37, Issue 7, 2013, Pages 5171-5183

  Xu, Yejun ^a   Wang, Huimin ^a  

^a HOHAI UNIVERSITY   (China)

Author keywords

Consistency test; Eigenvector method; Incomplete fuzzy preference relation; Inconsistency repairing; Multiplicative consistency

Indexed keywords

CONSISTENCY TESTS; EIGENVECTOR METHODS; INCOMPLETE FUZZY PREFERENCE RELATION; INCONSISTENCY REPAIRING; MULTIPLICATIVE CONSISTENCY;

COMPUTER SIMULATION; MATHEMATICAL MODELS;

REPAIR;

EID: 84872595038     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2012.10.008     Document Type: Article

References (47)

1. Chiclana F., Herrera F., Herrera-Viedma E. Integrating multiplicative preference relations in a multipurpose decision-making model based on fuzzy preference relations. Fuzzy Sets Syst. 2001, 122:277-291.
2. Herrera-Viedma E., Herrera F., Chiclana F., Luque M. Some issues on consistency of fuzzy preference relations. Eur. J. Oper. Res. 2004, 154:98-109.
3. Kacprzyk J. Group decision making with a fuzzy majority. Fuzzy Sets Syst. 1986, 18:105-118.
4. Lipovetsky S., Conklin W.M. Robust estimation of priorities in the AHP. Eur. J. Oper. Res. 2002, 137:110-122.
5. Ma J., Fan Z.P., Jiang Y.P., Mao J.Y., Ma L. A method for repairing the inconsistency of fuzzy preference relations. Fuzzy Sets Syst. 2006, 157:20-33.
6. Orlovsky S.A. Decision-making with a fuzzy preference relations. Fuzzy Sets Syst. 1978, 1:155-167.
7. Tanino T. Fuzzy preference orderings in group decision making. Fuzzy Sets Syst. 1984, 12:117-131.
8. Tanino T. Fuzzy preference relation in group decision making. Non-Conventional Preference Relation in Decision Making 1988, Springer, Berlin. J. Kacprzyk, M. Roubens (Eds.).
9. Tanino T. On group decision making under fuzzy preferences. Multiperson Decision Making Using Fuzzy Sets and Possibility Theory 1990, 172-185. Kluwer, Netherlands. J. Kacprzyk, M. Fedrizzi (Eds.).
10. Wang Y.M., Fan Z.P. Fuzzy preference relations: aggregation and weight determination. Comput. Ind. Eng. 2007, 53:163-172.
11. Wang Y.M., Fan Z.P. Group decision making based on fuzzy preference relations: logarithmic and geometric least squares methods. Appl. Math. Comput. 2007, 194:108-119.
12. Wang Y.M., Fan Z.P., Hua Z.S. A chi-square method for obtaining a priority vector from multiplicative and fuzzy preference relations. Eur. J. Oper. Res. 2007, 182:356-366.
13. Wang Y.M., Parkan C. Multiple attribute decision making based on fuzzy preference information on alternatives: ranking and weighting. Fuzzy Sets Syst. 2005, 153:331-346.
14. Wang Y.M., Parkan C. Optimal aggregation of fuzzy preference relations with an application to broadband internet service selection. Eur. J. Oper. Res. 2008, 187:1476-1486.
15. Xu Y.J., Da Q.L., Liu L.H. Normalizing rank aggregation method for priority of a fuzzy preference relation and its effectiveness. Int. J. Approx. Reason. 2009, 50:1287-1297.
16. Xu Z.S., Da Q.L. An approach to improving consistency of fuzzy preference matrix. Fuzzy Optimiz. Decision Making 2003, 2:3-12.
17. Xu Z.S., Da Q.L. A least deviation method to obtain a priority vector of a fuzzy preference relation. Eur. J. Oper. Res. 2005, 164:206-216.
18. Alonso S., Chiclana F., Herrera F., Herrera-Viedma E. A consistency-based procedure to estimate missing pairwise preference values. Int. J. Intell. Syst. 2008, 23:155-175.
19. Alonso S., Chiclana F., Herrera F., Herrera-Viedma E. A learning procedure to estimate missing values in fuzzy preference relations based on additive consistency. MDAI2004 2004, 227-238. Springer-Verlag, Berlin, Heidelberg. V. Torra, Y. Narukawa (Eds.).
20. Alonso S., Herrera-Viedma E., Chiclana F., Herrera F., Porcel C. Strategies to manage ignorance situations in multiperson decision making problems. MDAI 2006, LNAI 2006, 34-45. Springer-Verlag, Berlin, Heidelberg. V. Torra (Ed.).
21. M. Brunelli, M. Fedrizzi, S. Giove, Reconstruction methods for incomplete fuzzy preference relations: a numerical comparison, in: F. Masulli, S. Mitra, G. Pasi (Eds.), WILF 2007, LNAI, 2007, pp. 86-93.
22. Chiclana F., Herrera-Viedma E., Alonso S. A note on two methods for estimating missing pairwise preference values. IEEE Trans. Syst. Man Cybernet. - Part B: Cybernet. 2009, 39:1628-1633.
23. Chiclana F., Herrera-Viedma E., Alonso S., Herrera F. A note on the estimation of missing pairwise preference values: a U-consistency based method. Int. J. Uncertainty Fuzziness Knowledge-Based Syst. 2008, 16:19-32.
24. Chiclana F., Herrera F., Herrera-Viedma E. Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations. Fuzzy Sets Syst. 1998, 97:33-48.
25. Fedrizzi M., Silvio G. Incomplete pairwise comparison and consistency optimization. Eur. J. Oper. Res. 2007, 183:303-313.
26. Gong Z.W. Least-square method to priority of the fuzzy preference relations with incomplete information. Int. J. Approx. Reason. 2008, 47:258-264.
27. Herrera-Viedma E., Alonso S., Chiclana F., Herrera F. A consensus model for group decision making with incomplete fuzzy preference relations. IEEE Trans. Fuzzy Syst. 2007, 15:863-877.
28. Herrera-Viedma E., Chiclana F., Herrera F., Alonso S. Group decision-making model with incomplete fuzzy preference relations based on additive consistency. IEEE Trans. Syst. Man Cybernet. - Part B: Cybernet. 2007, 37:176-189.
29. Lee H.S., Chou M.T., Fang H.H., Tseng W.K., Yeh C.H. Estimating missing values in incomplete additive fuzzy preference relations. KES2007/WIRN2007, Part II, LNAI 2007, 1307-1314. Springer-Verlag, Berlin, Heidelberg. B. Apolloni (Ed.).
30. Liu X.W., Pan Y.W., Xu Y.J., Yu S. Least square completion and inconsistency repair methods for additively consistent fuzzy preference relations. Fuzzy Sets Syst. 2012, 198:1-19.
31. Xu Y.J. Logarithmic least squares method to priority for group decision making with incomplete fuzzy preference relations. Appl. Math. Model. 2012, http://dx.doi.org/10.1016/j.apm.2012.1005.101.
32. Xu Y.J., Da Q.L. Methods for priority of incomplete complementary judgement matrices. Syst. Eng. Electron. 2009, 31:95-99.
33. Xu Y.J., Da Q.L. Weighted least-square method and its improvement for priority of incomplete complementary judgement matrix. Syst. Eng. Electron. 2008, 31:1273-1276.
34. Xu Y.J., Da Q.L., Wang H.M. A note on group decision-making procedure based on incomplete reciprocal relations. Soft Comput. 2011, 15:1289-1300.
35. Xu Z.S. Goal programming models for obtaining the priority vector of incomplete fuzzy preference relation. Int. J. Approx. Reason. 2004, 36:261-270.
36. Xu Z.S. A procedure for decision making based on incomplete fuzzy preference relation. Fuzzy Optimiz. Decision Making 2005, 4:175-189.
37. Xu Z.S., Chen J. Group decision-making procedure based on incomplete reciprocal relations. Soft Comput. 2008, 12:515-521.
38. Saaty T.L. The Analytic Hierarchy Process 1980, McGraw-Hill, New York.
39. Basile L. Ranking alternatives by weak transitivity relation. Multiperson Decision Making Using Fuzzy Sets and Possibility Theory 1990, Kluwer, Netherlands. J. Kacprzyk, M. Fedrizzi (Eds.).
40. Karapetrovic S., Rosenbloom E.S. A quality control approach to consistency paradoxes in AHP. Eur. J. Oper. Res. 1999, 119:704-718.
41. Xu Z.S., Wei C.P. A consistency improving method in the analytic hierarchy process. Eur. J. Oper. Res. 1999, 116:443-449.
42. Saaty T.L. Eigenvector and logarithmic least squares. Eur. J. Oper. Res. 1990, 48:156-160.
43. Saaty T.L., Vargas L.G. Comparison of eigenvalue, logarithmic least squares and least squares methods in estimating ratios. Math. Model. 1984, 5:309-324.
44. Wang L.F., Xu S.B. The Introduction to Analytic Hierarchy Process 1990, China Renmin University, Beijing.
45. Xu Z.S. On consistency of the weighted geometric mean complex judgement matrix in AHP. Eur. J. Oper. Res. 2000, 126:683-687.
46. Jiang Y.P., Fan Z.P. An approach to group decision making based on incomplete fuzzy preference relations. Int. J. Uncertainty Fuzziness Knowledge-Based Syst. 2008, 16:83-94.
47. Harker P.T. Incomplete pairwise comparisons in the analytic hierarchy process. Math. Model. 1987, 9:837-848.