The multiplicative consistency index of hesitant fuzzy preference relation

IEEE Transactions on Fuzzy Systems

Volumn 24, Issue 1, 2016, Pages 82-93

  Liu, Haifeng ^a   Xu, Zeshui ^b   Liao, Huchang ^b  

^a PLA UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b Sichuan University   (China)

Author keywords

Decision making; Density functional theory; Euclidean distance; Fuzzy sets; Hafnium; Hamming distance; Indexes

Indexed keywords

DECISION MAKING; DECISION THEORY; FUZZY SETS; HAFNIUM; HAMMING DISTANCE;

CONSISTENCY CHECKING; CONSISTENCY INDEX; DECISION MAKERS; DISTANCE CALCULATION; EUCLIDEAN DISTANCE; FUZZY PREFERENCE RELATIONS; INDEXES; MULTIPLICATIVE CONSISTENCY;

DENSITY FUNCTIONAL THEORY;

EID: 84962109934     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2015.2426315     Document Type: Article

References (32)

1. V. Torra, "Hesitant fuzzy sets," Int. J. Intell. Syst., vol. 25, pp. 529-539, 2010
2. L. A. Zadeh, "Fuzzy sets," Inform. Control, vol. 8, pp. 338-353, 1965
3. V. Torra and Y. Narukawa, "On hesitant fuzzy sets and decision," in Proc. 18th IEEE Int. Conf. Fuzzy Syst., Jeju Island, Korea, 2009, pp. 1378-1382
4. M. M. Xia and Z. S. Xu, "Hesitant fuzzy information aggregation in decision making," Internal J. Approximate Reasoning, vol. 52, pp. 395-407, 2011
5. H. C. Liao and Z. S. Xu, "Subtraction and division operations over hesitant fuzzy sets," J. Intell. Fuzzy Syst., vol. 27, pp. 65-72, 2014
6. R. M. Rodríguez, L. Martínez, and F. Herrera, "Hesitant fuzzy linguistic terms sets for decision making," IEEE Trans. Fuzzy Syst., vol. 20, no. 1, pp. 109-119, Feb. 2012
7. G. Qian, H. Wang, and X. Q. Feng, "Generalized hesitant fuzzy sets and their application in decision support system," Knowl.-Based Syst., vol. 37, pp. 357-365, 2013
8. C. P. Wei, N. Zhao, and X. J. Tang, "Operators and comparisons of hesitant fuzzy linguistic term sets," IEEE Trans. Fuzzy Syst., vol. 22, no. 3, pp. 575-585, Jun. 2014
9. G. W. Wei, "Hesitant fuzzy prioritized operators and their application to multiple attribute decision making," Knowl.-Based Syst., vol. 31, pp. 176-182, 2012
10. Z. M. Zhang, "Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making," Inform. Sci., vol. 234, pp. 150-181, 2013
11. H. C. Liao and Z. S.Xu, "Some newhybrid weighted aggregation operators under hesitant fuzzy multi-criteria decisionmaking environment," J. Intell. Fuzzy Syst., vol. 26, no. 4, pp. 1601-1617, 2014
12. H. C. Liao and Z. S. Xu, "Extended hesitant fuzzy hybrid weighted aggregation operators and their application in decision making," Soft Comput., vol. 19, no. 9, pp. 2551-2564, 2015
13. Z. S. Xu and M. M. Xia, "Distance and similarity measures for hesitant fuzzy sets," Inform. Sci., vol. 181, pp. 2128-2138, 2011
14. N. Chen, Z. S. Xu, and M. M. Xia, "Correlation coefficients of hesitant fuzzy sets and their application to clustering analysis," Appl.Math. Model., vol. 37, pp. 2197-2211, 2013
15. H. C. Liao, Z. S. Xu, and X. J. Zeng, "Novel correlation coefficients between hesitant fuzzy sets and their application in decision making," Knowl.-Based Syst., vol. 82, pp. 115-127, 2015
16. Z. S. Xu and M. M. Xia, "Hesitant fuzzy entropy and cross-entropy and their use in multiattribute decision-making," Int. J. Intell. Syst., vol. 27, no. 9, pp. 799-822, 2012
17. B. Farhadinia, "Information measures for hesitant fuzzy sets and intervalvalued hesitant fuzzy sets," Inform. Sci., vol. 240, pp. 129-144, 2013
18. H. C. Liao and Z. S. Xu, "A VIKOR-based method for hesitant fuzzy multi-criteria decision making," Fuzzy Optim. Decision Making, vol. 12, no. 4, pp. 373-392, 2013
19. X. L. Zhang and Z. S. Xu, "The TODIM analysis approach based on novel measured functions under hesitant fuzzy environment," Knowl.-Based Syst., vol. 61, pp. 48-58, 2014
20. H. C. Liao and Z. S. Xu, "Satisfaction degree based interactive decision making method under hesitant fuzzy environment with incomplete weights," Int. J. Uncertainty, Fuzziness Knowl.-Based Syst., vol. 22, no. 4, pp. 553-572, 2014
21. D. J.Yu,W.Y. Zhang, andY. J.Xu, "Group decisionmaking under hesitant fuzzy environment with application to personnel evaluation," Knowl.-Based Syst., vol. 52, pp. 1-10, 2013
22. H. C. Liao, Z. S.Xu, andM.M.Xia, "Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making," Int. J. Inform. Technol. Decision Making, vol. 13, no. 1, pp. 47-76, 2014
23. T. Tanio, "Fuzzy preference orderings in group decision making," Fuzzy Sets Syst., vol. 12, pp. 117-131, 1984
24. 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
25. 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., vol. 157, pp. 20-33, 2006
26. S. Genc', F. E. Boran, D. Akay, and Z. S. Xu, "Interval multiplicative transitivity for consistency, missing values and priority weights of interval fuzzy preference relations," Inform. Sci., vol. 180, pp. 4877-4891, 2010
27. Y. C. Dong, Y. F. Xu, and H. Y. Li, "On consistency measures of linguistic preference relations," Eur. J. Oper. Res., vol. 189, pp. 430-444, 2008
28. Z. W. Gong, L. S. Li, J. Cao, and F. X. Zhou, "On additive consistent properties of the intuitionistic fuzzy preference relation," Int. J. Inform. Technol. Decision Making, vol. 9, pp. 1009-1025, 2010
29. Z. W. Gong, L. S. Li, J. Forrest, and Y. Zhao, "The optimal priority models of the intuitionistic fuzzy preference relation and their application in selecting industries with highermeteorological sensitivity," Expert Syst. Appl., vol. 38, pp. 4394-4402, 2011
30. Z. J. Wang, "Derivation of intuitionistic fuzzy weights based on intuitionistic fuzzy preference relations," Appl. Math. Model., vol. 37, pp. 6377-6388, 2013
31. Z. S. Xu and H. C. Liao, "Intuitionistic fuzzy analytic hierarchy process," IEEE Trans. Fuzzy Syst., vol. 22, no. 4, pp. 749-761, Aug. 2014
32. O. Ngwenyama and N. Bryson, "Eliciting and mapping qualitative preferences to numeric rankings in group decision-making," Eur. J. Oper. Res., vol. 116, pp. 487-497, 1999