Least square completion and inconsistency repair methods for additively consistent fuzzy preference relations

Fuzzy Sets and Systems

Volumn 198, Issue , 2012, Pages 1-19

  Liu, Xinwang ^a   Pan, Yuwen ^a   Xu, Yejun ^b   Yu, Shui ^c  

^a Southeast University   (China)

^b HOHAI UNIVERSITY   (China)

^c DEAKIN UNIVERSITY   (Australia)

Author keywords

Additively consistent; Fuzzy preference relations; Group decision making (GDM); Incomplete information

Indexed keywords

ADDITIVE CONSISTENCY; ADDITIVELY CONSISTENT; CONSISTENT FUZZY PREFERENCE RELATION; FUZZY PREFERENCE RELATIONS; GROUP DECISION MAKING; INCOMPLETE INFORMATION; LEAST SQUARE; NUMERICAL EXAMPLE; REPAIR METHODS; SUFFICIENT AND NECESSARY CONDITION;

DECISION MAKING;

LEAST SQUARES APPROXIMATIONS;

EID: 84859587805     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2011.11.009     Document Type: Article

References (52)

1. S. Alonso, Group Decision Making with Incomplete Fuzzy Preference Relations, Ph.D. Thesis, University of Granada, 2006.
2. S. Alonso, F. Chiclana, F. Herrera, and E. Herrera-Viedma A learning procedure to estimate missing values in fuzzy preference relations based on additive consistency V. Torra, Y. Narukawa, MDAI 2004, Lecture Notes in Artificial Intelligence vol. 3131 2004 Springer-Verlag Berlin, Heidelberg 227 238
3. S. Alonso, F. Chiclana, F. Herrera, E. Herrera-Viedma, J. Alcalá-Fdez, and C. Porcel A consistency-based procedure to estimate missing pairwise preference values Int. J. Intelligent Syst. 23 2 2008 155 175
4. S. Alonso, E. Herrera-Viedma, F. Chiclana, and F. Herrera Individual and social strategies to deal with ignorance situations in multi-person decision making Int. J. Inf. Technol. Decision Making 8 2 2009 313 333
5. F.T.S. Chan, N. Kumar, M. Tiwari, H. Lau, and K.L. Choy Global supplier selection: a fuzzy-AHP approach Int. J. Prod. Res. 46 14 2008 3825 3857
6. K. Charnpratheep, Q. Zhou, and B. Garner Preliminary landfill site screening using fuzzy geographical information systems Waste Manage. Res. 15 2 1997 197 215
7. 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. 97 1998 33 48
8. F. Chiclana, F. Herrera, and E. Herrera-Viedma Integrating multiplicative preference relations in a multipurpose decision-making model based on fuzzy preference relations Fuzzy Sets Syst. 122 2001 277 291
9. F. Chiclana, E. Herrera-Viedma, S. Alonso, and F. Herrera Consistency of reciprocal preference relations Proceedings of the 2007 IEEE International Conference on Fuzzy Systems 2007
10. B. De Baets, and H. De Meyer Transitivity frameworks for reciprocal relations: cycle-transitivity versus fg-transitivity Fuzzy Sets Syst. 152 2 2005 249 270
11. B. De Baets, H. De Meyer, and K. De Loof On the cycle-transitivity of the mutual rank probability relation of a poset Fuzzy Sets Syst. 161 2010 2695 2708
12. B. De Baets, H. De Meyer, B. De Schuymer, and S. Jenei Cyclic evaluation of transitivity of reciprocal relations Soc. Choice Welfare 26 2 2006 217 238
13. B. De Baets, S. Janssens, and H. De Meyer On the transitivity of a parametric family of cardinality-based similarity measures Int. J. Approx. Reason. 50 1 2009 104 116
14. Y. Dong, Y. Xu, and H. Li On consistency measures of linguistic preference relations Eur. J. Oper. Res. 189 2 2008 430 444
15. D. Dubois, and H. Prade Possibility theory as a basis for preference propagation in automated reasoning 1992 IEEE International Conference on Fuzzy Systems - FUZZ-IEEE 1992 821 832
16. D. Dubois, and H. Prade An introduction to bipolar representations of information and preference Int. J. Intelligent Syst. 23 8 2008 866 877
17. I. Erturul, and N. Karakaolu Performance evaluation of Turkish cement firms with fuzzy analytic hierarchy process and TOPSIS methods Expert Syst. Appl. 36 1 2009 702 715
18. Z.-P. Fan, S.-H. Xiao, and G.-F. Hu An optimization method for integrating two kinds of preference information in group decision making Comput. Ind. Eng. 46 2 2004 329 335
19. M. Fedrizzi, and M. Brunelli On the normalisation of a priority vector associated with a reciprocal relation Int. J. Gen. Syst. 38 5 2009 579 586
20. M. Fedrizzi, and S. Giove Incomplete pairwise comparison and consistency optimization Eur. J. Oper. Res. 183 1 2007 303 313
21. J.C. Fodor, and M. Roubens Fuzzy Preference Modelling and Multicriteria Decision Support 1994 Kluwer Dordrecht
22. Z.-W. Gong Least-square method to priority of the fuzzy preference relations with incomplete information Int. J. Approx. Reason. 47 2 2008 258 264
23. 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. 15 5 2007 863 877
24. E. Herrera-Viedma, F. Chiclana, F. Herrera, and S. Alonso Group decision-making model with incomplete fuzzy preference relations based on additive consistency IEEE Trans. Syst. Man Cybern. Part B - Cybern. 37 1 2007 176 189
25. E. Herrera-Viedma, F. Herrera, F. Chiclana, and M. Luque Some issues on consistency of fuzzy preference relations Eur. J. Oper. Res. 154 1 2004 98 109
26. Y.-P. Jiang, and Z.-P. Fan An approach to group decision making based on incomplete fuzzy preference relations Int. J. Uncertainty Fuzziness Knowl. Based Syst. 16 1 2008 83 94
27. J. Kacprzyk Group decision making with a fuzzy linguistic majority Fuzzy Sets Syst. 18 2 1986 105 118
28. S.-H. Kim, and B.-S. Ahn Group decision making procedure considering preference strength under incomplete information Comput. Oper. Res. 24 1997 1101 1112
29. S.H. Kim, and C.H. Han An interactive procedure for multi-attribute group decision making with incomplete information Comput. Oper. Res. 26 1999 755 772
30. H.-S. Lee, M.-T. Chou, H.-H. Fang, W.-K. Tseng, and C.-H. Yeh Estimating missing values in incomplete additive fuzzy preference relations KES 2007/WIRN 2007, Part II, Lecture Notes in Artificial Intelligence vol. 4693 2007 Springer-Verlag Berlin, Heidelberg 1307 1314
31. S. Lipovetsky, and M.M. Conklin Robust estimation of priorities in the AHP Eur. J. Oper. Res. 137 1 2002 110 122
32. J. Ma, Z.-P. Fan, Y.-P. Jiang, J.-Y. Mao, and L. Ma A method for repairing the inconsistency of fuzzy preference relations Fuzzy Sets Syst. 157 1 2006 20 33
33. H. Nurmi Approaches to collective decision making with fuzzy preference relations Fuzzy Sets Syst. 6 3 1981 249 259
34. S. Önüt, S.S. Kara, and E. Iik Long term supplier selection using a combined fuzzy MCDM approach: a case study for a telecommunication company Expert Syst. Appl. 36 2 part 2 2009 3887 3895
35. S. Orlovsky Decision-making with a fuzzy preference relation Fuzzy Sets Syst. 1 3 1978 155 167
36. 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. 79 1994 249 265
37. T.L. Saaty The Analytic Hierarchy Process 1980 McGraw-Hill New York
38. B. Srdjevic Combining different prioritization methods in the analytic hierarchy process synthesis Comput. Oper. Res. 32 7 2005 1897 1919
39. T. Tanino Fuzzy preference orderings in group decision making Fuzzy Sets Syst. 12 1984 117 131
40. T.-C. Wang, and T.-H. Chang Forecasting the probability of successful knowledge management by consistent fuzzy preference relations Expert Syst. Appl. 32 3 2007 801 813
41. Y.-M. Wang, J.-B. Yang, and D.-L. Xu Interval weight generation approaches based on consistency test and interval comparison matrices Appl. Math. Comput. 167 1 2005 252 273
42. D.D. Wu Performance evaluation: an integrated method using data envelopment analysis and fuzzy preference relations Eur. J. Oper. Res. 194 1 2009 227 235
43. Y. Xu, Q. Da, and L. Liu Normalizing rank aggregation method for priority of a fuzzy preference relation and its effectiveness Int. J. Approx. Reason. 50 8 2009 1287 1297
44. Z.S. Xu Goal programming models for obtaining the priority vector of incomplete fuzzy preference relation Int. J. Approx. Reason. 36 3 2004 261 270
45. Z.S. Xu A procedure for decision making based on incomplete fuzzy preference relation Fuzzy Optim. Decision Making 4 2005 175 189
46. Z.S. Xu A survey of preference relations Int. J. Gen. Syst. 36 2 2007 179 203
47. Z.S. Xu, and J. Chen Group decision-making procedure based on incomplete reciprocal relations Soft Comput. 12 6 2008 515 521
48. Z.S. Xu, and J. Chen Some models for deriving the priority weights from interval fuzzy preference relations Eur. J. Oper. Res. 184 2008 266 280
49. Z.S. Xu, and Q.L. Da An approach to improving consistency of fuzzy preference matrix Fuzzy Optim. Decision Making 2 1 2003 3 12
50. Z.S. Xu, and Q.L. Da A least deviation method to obtain a priority vector of a fuzzy preference relation Eur. J. Oper. Res. 164 2005 206 216
51. Z.S. Xu, and C.P. Wei A consistency improving method in the analytic hierarchy process Eur. J. Oper. Res. 116 2 1999 443 449
52. M. Zerafat Angiz, L.A. Emrouznejad, A. Mustafa, and A.R. Komijan Selecting the most preferable alternatives in a group decision making problem using DEA Expert Syst. Appl. 36 2009 9599 9602