Derivation of intuitionistic fuzzy weights based on intuitionistic fuzzy preference relations

Applied Mathematical Modelling

Volumn 37, Issue 9, 2013, Pages 6377-6388

  Wang, Zhou Jing ^a,b  

^a SHANGHAI UNIVERSITY   (China)

^b ZHEJIANG UNIVERSITY OF FINANCE AND ECONOMICS   (China)

Author keywords

Additive consistency; Intuitionistic fuzzy preference relation; Intuitionistic fuzzy weight; Linear goal programming; Weak transitivity

Indexed keywords

ADDITIVE CONSISTENCY; INTUITIONISTIC FUZZY; INTUITIONISTIC FUZZY PREFERENCE RELATIONS; LINEAR GOAL PROGRAMMING; WEAK TRANSITIVITY;

COMPUTER SIMULATION; MATHEMATICAL MODELS;

FUZZY SETS;

EID: 84875377360     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2013.01.021     Document Type: Article

References (45)

1. Saaty T.L. The Analytic Hierarchy Process 1980, McGraw-Hill, New York.
2. Awasthi A., Chauhan S.S. A hybrid approach integrating affinity diagram, AHP and fuzzy TOPSIS for sustainable city logistics planning. Appl. Math. Model. 2012, 36:573-584.
3. Chang T.H. A method of fuzzy preference relation to authorize the worldwide interoperability for microwave access license in Taiwan. Appl. Math. Model. 2012, 36:3856-3869.
4. Chen Y.H., Chao R.J. Supplier selection using consistent fuzzy preference relations. Expert Syst. Appl. 2012, 39:3233-3240.
5. Chen S.M., Niou S.J. Fuzzy multiple attributes group decision-making based on fuzzy preference relations. Expert Syst. Appl. 2011, 38:3865-3872.
6. Chiclana F., Herrera-Viedma E., Alonso S., Herrera F. Cardinal consistency of reciprocal preference relations: a characterization of multiplicative transitivity. IEEE Trans. Fuzzy Syst. 2009, 17:14-23.
7. Díaz S., García-Lapresta J.L., Montes S. Consistent models of transitivity for reciprocal preferences on a finite ordinal scale. Inf. Sci. 2008, 178:2832-2848.
8. Herrera-Viedma E., Chiclana F., Herrera F., Alonso S. Group decision-making model with incomplete fuzzy preference relations based on additive consistency. IEEE Trans. Sys. Man Cybernet. - Part B: Cybernet. 2007, 37:176-189.
9. 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.
10. Liu X., Pan Y., Xu Y., Yu S. Least square completion and inconsistency repair methods for additively consistent fuzzy preference relations. Fuzzy Sets Syst. 2012, 198:1-19.
11. Xu Y., Patnayakuni R., Wang H. Logarithmic least squares method to priority for group decision making with incomplete fuzzy preference relations. Appl. Math. Model. 2013, 37:2139-2152.
12. Xu Z., Cai X. Group consensus algorithms based on preference relations. Inf. Sci. 2011, 181:150-162.
13. Xu Z., Chen J. MAGDM linear-programming models with distinct uncertain preference structures. IEEE Trans. Syst. Man Cybernet. Part B -Cybernet. 2008, 38:1356-1370.
14. Xu Z. A survey of preference relations. Int. J. Gen Syst 2007, 36:179-203.
15. Saaty T.L., Vargas L.G. Uncertainty and rank order in the analytic hierarchy process. Eur. J. Oper. Res. 1987, 32:107-117.
16. Xu Z. On compatibility of interval fuzzy preference matrices. Fuzzy Optim. Decis. Making 2004, 3:217-225.
17. Van Laarhoven P.J.M., Pedrycz W. A fuzzy extension of Saaty's priority theory. Fuzzy Sets Syst. 1983, 11:229-241.
18. Wang Y.M., Elhag T.M.S. A goal programming method for obtaining interval weights from an interval comparison matrix. Eur. J. Oper. Res. 2007, 177:458-471.
19. Wang Y.M., Yang J.B., Xu D.L. A two-stage logarithmic goal programming method for generating weights from interval comparison matrices. Fuzzy Sets Syst. 2005, 152:475-498.
20. Liu F. Acceptable consistency analysis of interval reciprocal comparison matrices. Fuzzy Sets Syst. 2009, 160:2686-2700.
21. Xu Z., Chen J. Some models for deriving the priority weights from interval fuzzy preference relations. Eur. J. Oper. Res. 2008, 184:266-280.
22. Wang Z.J., Li K.W. Goal programming approaches to deriving interval weights based on interval fuzzy preference relations. Inf. Sci. 2012, 193:180-198.
23. Atanassov K. Intuitionistic fuzzy sets. Fuzzy Sets Syst. 1986, 20:87-96.
24. Chen S.M., Tan J.M. Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst. 1994, 67:163-172.
25. Chen Z., Yang W. A new multiple attribute group decision making method in intuitionistic fuzzy setting. Appl. Math. Model. 2011, 35:4424-4437.
26. Hong D.H., Choi C.H. Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst. 2000, 114:103-113.
27. Park J.H., Park I.Y., Kwun Y.C., Tan X. Extension of the TOPSIS method for decision making problems under interval-valued intuitionistic fuzzy environment. Appl. Math. Model. 2011, 35:2544-2556.
28. Li D.F. Multiattribute decision making models and methods using intuitionistic fuzzy sets. J. Comput. Syst. Sci. 2005, 70:73-85.
29. Li D.F., Chen G.H., Huang Z.G. Linear programming method for multiattribute group decision making using IF sets. Inf. Sci. 2010, 180:1591-1609.
30. Vahdani B., Meysam Mousavi S., Tavakkoli-Moghaddam R., Hashemi H. A new design of the elimination and choice translating reality method for multi-criteria group decision-making in an intuitionistic fuzzy environment. Appl. Math. Model. 2013, 37:1781-1799.
31. Wang Z.J., Qian E.Y. A vague-set-based fuzzy multi-objective decision making model for bidding purchase. J. Zhejiang Univ. Sci. A 2007, 8:644-650.
32. Wang Z.J., Li K.W., Wang W. An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights. Inf. Sci. 2009, 179:3026-3040.
33. Wang Z.J., Li K.W., Xu J. A mathematical programming approach to multi-attribute decision making with interval-valued intuitionistic fuzzy assessment information. Expert Syst. Appl. 2011, 38:12462-12469.
34. Wu J., Cao Q.W. Same families of geometric aggregation operators with intuitionistic trapezoidal fuzzy numbers. Appl. Math. Model. 2013, 37:318-327.
35. Ye J. Multicriteria decision-making method using the Dice similarity measure based on the reduct intuitionistic fuzzy sets of interval-valued intuitionistic fuzzy sets. Appl. Math. Model. 2012, 36:4466-4472.
36. Szmidt E., Kacprzyk J. A consensus-reaching process under intuitionistic fuzzy preference relations. Int. J. Intell. Syst. 2003, 18:837-852.
37. Xu Z., Yager R.R. Intuitionistic and interval-valued intuitionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optim. Decis. Making 2009, 8:123-139.
38. Xu Z. Intuitionistic preference relations and their application in group decision making. Inf. Sci. 2007, 177:2363-2379.
39. Xu Z., Cai X., Szmidt E. Algorithms for estimating missing elements of incomplete intuitionistic preference relations. Int. J. Intell. Syst. 2011, 26:787-813.
40. Xu Z. An error-analysis-based method for the priority of an intuitionistic fuzzy preference relation in decision making. Knowl.-Based Syst. 2012, 33:173-179.
41. Gong Z.W., Li L.S., Zhou F.X., Yao T.X. Goal programming approaches to obtain the priority vectors from the intuitionistic fuzzy preference relations. Comput. Ind. Eng. 2009, 57:1187-1193.
42. Gong Z.W., Li L.S., Forrest J., Zhao Y. The optimal priority models of the intuitionistic fuzzy preference relation and application in selecting industries with higher meteorological sensitivity. Expert Syst. Appl. 2011, 38:4394-4402.
43. Tanino T. Fuzzy preference orderings in group decision making. Fuzzy Sets Syst. 1984, 12:117-131.
44. Xu Z., Yager R.R. Some geometric aggregation operators based intuitionistic fuzzy sets. Int. J. Gen. Syst. 2006, 35:417-433.
45. Sugihara K., Ishii H., Tanaka H. Interval priorities in AHP by interval regression analysis. Eur. J. Oper. Res. 2004, 158:745-754.