Some hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group decision making

IEEE Transactions on Fuzzy Systems

Volumn 22, Issue 1, 2014, Pages 83-97

  Liu, Peide ^a  

^a SHANDONG UNIVERSITY OF FINANCE AND ECONOMICS   (China)

Author keywords

Group decision making; Hamacher aggregation operators; interval valued intuitionistic fuzzy numbers (IVIFNs); multiple attribute decision making (MADM)

Indexed keywords

EID: 84893108445     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2013.2248736     Document Type: Article

References (35)

1. K.T. Atanassov, "Intuitionistic fuzzy sets, " Fuzzy Sets Syst., vol. 20, pp. 87-96, 1986.
2. K. T. Atanassov, "More on intuitionistic fuzzy sets, " Fuzzy Sets Syst., vol. 33, pp. 37-46, 1989.
3. K. T. Atanassov, "Operators over interval-valued intuitionistic fuzzy sets, " Fuzzy Sets Syst., vol. 64, pp. 159-174, 1994.
4. K. T. Atanassov and G. Gargov, "Interval-valued intuitionistic fuzzy sets, " Fuzzy Sets Syst., vol. 3, pp. 343-349, 1989.
5. G. Beliakov, H. Bustince, S. James, T. Calvo, and J. Fernandez, "Aggregation for Atanassov's intuitionistic and interval valued fuzzy sets: The median operator, " IEEE Trans. Fuzzy Syst., vol. 20, no. 3, pp. 487-498, Jun. 2012.
6. G. Beliakov, A. Pradera, and T. Calvo, Aggregation Functions: A Guide For Practitioners. Heidelberg, Germany: Springer, 2007.
7. G. Deschrijver, C. Cornelis, and E. E. Kerre, "On the representation of intuitionistic fuzzy t-norms and t-conorms, " IEEE Trans. Fuzzy Syst., vol. 12, no. 1, pp. 45-61, Feb. 2004.
8. G. Deschrijver and E. E Kerre, "A generalization of operators on intuition-istic fuzzy sets using triangular norms and conorms, " Notes Intuitionistic Fuzzy Sets, vol. 8, no. 1, pp. 19-27, 2002.
9. V. L. Gomathi Nayagam, S. Muralikrishnan, and G. Sivaraman "Multi-criteria decision making method based on interval-valued intuitionistic fuzzy sets, " Expert Syst. Appl., vol. 38, no. 3, pp. 1464-1467, 2011.
10. H. Hamachar, "Uber logische verknunpfungenn unssharfer Aussagen und deren Zugenhorige Bewertungsfunktione, " in Progress in Cybernat-ics and Systems Research, R. Trappl, G. H. Klir, and L. Riccardi, Eds. Washington, DC, USA: Hemisphere, 1978, vol. 3, pp. 276-288.
11. W. L. Hung and J. W. Wu, "Correlation of intuitionistic fuzzy sets by centroid method, " Inf. Sci., vol. 144, no. 1, pp. 219-225, 2002.
12. D. F. Li, "Multiattribute decision making method based on generalized OWA operators with intuitionistic fuzzy sets, " Expert Syst. Appl., vol. 37, no. 12, pp. 8673-8678, 2010.
13. D. F. Li, "TOPSIS-based nonlinear-programming methodology for mul-tiattribute decision making with interval-valued intuitionistic fuzzy sets, " IEEE Trans. Fuzzy Syst., vol. 18, no. 2, pp. 299-311, Apr. 2010.
14. D. F. Li, "The GOWA operator based approach to multiattribute decision making using intuitionistic fuzzy sets, " Math. Comput. Model., vol. 53, no. 5/6, pp. 1182-1196, 2011.
15. X. D. Liu, S. H. Zheng, and F. I. Xiong, "Entropy and subsethood for general interval-valued intuitionistic fuzzy sets, " in Fuzzy Systems and Knowledge Discovery, L. Wang and Y. Jin, Eds. Heidelberg, Germany: Springer, 2005, vol. 3613, pp. 42-52.
16. S. Roychowdhury and B.H. Wang, "On generalized Hamacher families of triangular operators, " Int. J. Approx. Reason., vol. 19, pp. 419-439, 1998. (Pubitemid 128426489)
17. C. Tan and Q. Zhang, "Fuzzy multiple attribute decision making based on interval valued intuitionistic fuzzy sets, " in Proc. IEEE Int. Conf. Syst., Man, Cybern., vol. 2, Taipei, Taiwan, 2006, pp. 1404-1407.
18. J. Q. Wang, K. J. Li, and H. Y. Zhang, "Interval-valued intuitionistic fuzzy multi-criteria decision-making approach based on prospect score function, " Knowl.-Based Syst., vol. 27, pp. 119-125, 2012.
19. W. Wang and X. Liu, "Intuitionistic fuzzy information aggregation using Einstein operations, " IEEE Trans. Fuzzy Syst., vol. 20, no. 5, pp. 923-938, Oct. 2012.
20. W. Z. Wang and X. W. Liu, "Intuitionistic fuzzy geometric aggregation operators based on Einstein operations, " Int. J. Intell. Syst., vol. 26, pp. 1049-1075, 2011.
21. Z. Wang and J. Xu, "A fractional programming method for interval-valued intuitionistic fuzzy multi-attribute decision making, " in Proc. 49th IEEE Int. Conf. Decision Control, 2010, pp. 636-641.
22. G. W. Wei and W. D. Yi, "Induced interval-valued intuitionistic fuzzy OWG operator, " in Proc. 5th Int. Conf. Fuzzy Syst. Knowl. Discovery, 2008, pp. 605-609.
23. M. M. Xia, Z. S. Xu, and B. Zhu, "Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm, " Knowl.-Based Syst., vol. 31, pp. 78-88, 2012.
24. Z. S. Xu, "An overview of methods for determining OWA weights, " Int. J. Intell. Syst., vol. 20, pp. 843-865, 2005.
25. Z. S. Xu, "Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making, " Control Decision, vol. 22, no. 2, pp. 215-219, 2007.
26. Z. S. Xu and J. Chen, "On geometric aggregation over interval-valued intuitionistic fuzzy information, " in Proc. 4th Int. Conf. Fuzzy Syst. Knowl. Discovery, 2007, pp. 466-471. (Pubitemid 351710790)
27. Z. S. Xu and J. Chen, "Approach to group decision making based on interval-valued intuitionistic judgment matrices, " Syst. Eng.-Theory Practice, vol. 27, no. 4, pp. 126-133, 2007. (Pubitemid 46812575)
28. Z. S. Xu and R. R. Yager, "Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group, " Fuzzy Optimization Decision Making, vol. 8, pp. 123-139, 2009.
29. R. R. Yager, "On ordered weighted averaging aggregation operators in multicriteria decision making, " IEEE Trans. Syst., Man Cybern., vol. 18, no. 1, pp. 183-190, Jan/Feb. 1988.
30. D. J. Yu, "Group decision making based on generalized intuitionistic fuzzy prioritized geometric operator, " Int. J. Intell. Syst., vol. 27, pp. 635-661, 2012.
31. D. J. Yu, Y. Y Wu, and T. Lu, "Interval-valued intuitionistic fuzzy prioritized operators and their application in group decision making, " Knowl.-Based Syst., vol. 30, pp. 57-66, 2012.
32. Z. L. Yue, "Deriving decision maker's weights based on distance measure for interval-valued intuitionistic fuzzy group decision making, " Expert Syst. Appl., vol. 38, pp. 11665-11670, 2011.
33. L. A. Zadeh, "Fuzzy sets, " Inf. Control, vol. 8, pp. 338-356, 1965.
34. H. Y Zhang, W. X. Zhang, and C. L. Mei, "Entropy of interval-valued fuzzy sets based on distance and its relationship with similarity measure, " Knowl.-Based Syst., vol. 22, pp. 449-454, 2009.
35. H. Zhao, Z. S. Xu, M. F. Ni, and S. S. Liu, "Generalized aggregation operators for intuitionistic fuzzy sets, " Int. J. Intell. Syst., vol. 25, pp. 1-30, 2010.