Some generalized neutrosophic number hamacher aggregation operators and their application to group decision making

International Journal of Fuzzy Systems

Volumn 16, Issue 2, 2014, Pages 242-255

  Liu, Peide ^a,b   Chu, Yanchang ^a   Li, Yanwei ^a   Chen, Yubao ^a  

^a CIVIL AVIATION UNIVERSITY OF CHINA   (China)

^b SHANDONG UNIVERSITY OF FINANCE AND ECONOMICS   (China)

Author keywords

Generalized aggregation operator; Group decision making; Hamacher aggregation operator; Neutrosophic set (NS)

Indexed keywords

MATHEMATICAL OPERATORS; STATISTICAL METHODS;

AGGREGATION OPERATOR; AVERAGING OPERATORS; GENERALIZED AGGREGATION OPERATOR; GROUP DECISION MAKING; HAMACHE AGGREGATION OPERATOR; INCOMPLETE INFORMATION; NEUTROSOPHIC SET; NEUTROSOPHIC SETS; PROPERTY;

DECISION MAKING;

EID: 84904958948     PISSN: 15622479     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (38)

1. L. A. Zadeh, "Fuzzy sets," Information and Control, vol. 8, no.3, pp. 338-356, 1965.
2. K. T. Atanassov, "Intuitionistic fuzzy sets," Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87-96, 1986.
3. K. T. Atanassov, "More on intuitionistic fuzzy sets," Fuzzy Sets and Systems, vol. 33, no. 1, pp. 37-46, 1989.
4. F. Smarandache, A unifying field in logics. neutrosophy: Neutrosophic probability, set and logic, American Research Press, Rehoboth, 1999.
5. H. Wang, F. Smarandache, Y. Zhang, and R. Sunderraman, "Single valued neutrosophic sets," in Proc. of 10th 476 Int. Conf. on Fuzzy Theory and Technology, Salt Lake City, 477 Utah, 2005.
6. J. Ye, "Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment," International Journal of General Systems, vol. 42, no. 4, pp. 386-394, 2013.
7. K. T. Atanassov and G. Gargov, "Interval-valued intuitionistic fuzzy sets," Fuzzy Sets and Systems, vol. 31, no. 3, pp. 343-349, 1989.
8. K. T. Atanassov, "Operators over interval-valued intuitionistic fuzzy sets," Fuzzy Sets and Systems, vol. 64, no. 2, pp. 159-174, 1994.
9. H. Wang, F. Smarandache, and Y. Q. Zhang, Interval neutrosophic sets and logic: Theory and applications in computing, Hexis, Phoenix, AZ, 2005.
10. J. Ye, "Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making," Journal of Intelligent & Fuzzy Systems, vol. 26, no. 1, pp. 165-172, 2014.
11. Y. Guo, H. D. Cheng, Y. Zhang, and W. Zhao, "A new neutrosophic approach to image denoising," New Mathematics and Natural Computation, vol. 5, no. 3, pp. 653-662, 2009.
12. Y. Guo and H. D. Cheng, "New neutrosophic approach to image segmentation," Pattern Recognition, vol. 42, no. 5, pp. 587-595, 2009.
13. R. R. Yager, "On ordered weighted averaging aggregation operators in multicriteria decision making," IEEE Trans. on Systems, Man and Cybernetics, vol. 18, no. 1, pp. 183-190, 1988.
14. Z. S. Xu, "Intuitionistic fuzzy aggregation operators," IEEE Trans. on Fuzzy Systems, vol. 15, no. 6, pp. 1179-1187, 2007.
15. Z. S. Xu and R. R. Yager, "Some geometric aggregation operators based on intuitionistic fuzzy sets," International Journal of General Systems, vol. 35, no. 4, pp. 417-433, 2006.
16. H. Zhao, Z. S. Xu, M. F. Ni, and S. S. Liu, "Generalized aggregation operators for intuitionistic fuzzy sets," International Journal of Intelligent Systems, vol. 25, no. 1, pp. 1-30, 2010.
17. M. M. Xia, Z. S. Xu, and B. Zhu, "Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm," Knowledge- Based Systems, vol. 31, no. 1, pp. 78-88, 2012.
18. D. J. Yu, "Group decision making based on generalized intuitionistic fuzzy prioritized geometric operator," International Journal of Intelligent Systems, vol. 27, no. 7, pp. 635-661, 2012.
19. W. Z. Wang and X. W. Liu, "Intuitionistic fuzzy geometric aggregation operators based on Einstein operations," International Journal of Intelligent Systems, vol. 26, no. 11, pp. 1049-1075, 2011.
20. G. Beliakov, A. Pradera, and T. Calvo, Aggregation Functions: A Guide for Practitioners, Springer, Heidelberg, Berlin, New York, 2007.
21. P. D. Liu, "Some Hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to Group Decision Making," IEEE Trans. on Fuzzy systems, vol. 22, no. 1, pp. 83-97, 2014.
22. D. J. Yu, "Multi-criteria decision making based on generalized prioritized aggregation operators under intuitionistic fuzzy environment," International Journal of Fuzzy Systems, vol. 15, no. 1, pp. 47-54, 2013.
23. B. Q. Hu and H. Wong, "Generalized interval- valued fuzzy rough sets based on interval- valued fuzzy logical operators," International Journal of Fuzzy Systems, vol. 15, no. 4, pp. 381-391, 2013.
24. Y. D. He, H. Y. Chen, and L. G. Zhou, "Generalized interval-valued Atanassov's intuitionistic fuzzy power operators and their application to group decision making," International Journal of Fuzzy Systems, vol. 15, no. 4, pp. 401-411, 2013.
25. P. D. Liu and Y. Liu, "An approach to multiple attribute group decision making based on intuitionistic trapezoidal fuzzy power generalized aggregation operator," International Journal of Computational Intelligence Systems, vol. 7, no. 2, pp. 291-304, 2014.
26. P. D. Liu and Y. M. Wang, "Multiple attribute group decision making methods based on intuitionistic linguistic power generalized aggregation operators," Applied soft computing, vol. 17, no. 1, pp. 90-104, 2014.
27. P. D. Liu, Z. Liu, and X. Zhang, "Some intuitionistic uncertain linguistic Heronian mean operators and their application to group decision making," Applied Mathematics and Computation, vol. 230, pp. 570-586, 2014.
28. P. D. Liu and X. C. Yu, "2-dimension uncertain linguistic power generalized weighted aggregation operator and its application for multiple attribute group decision making," Knowledge-based systems, vol. 57, no. 1, pp. 69-80, 2014.
29. P. D. Liu, "Some generalized dependent aggregation operators with intuitionistic linguistic numbers and their application to group decision making," Journal of Computer and System Sciences, vol. 79, no. 1, pp. 131-143, 2013.
30. A. Robinson, Non-standard analysis, North-Holland Pub. Co., 1966.
31. H. Y. Zhang, J. Q. Wang, and X. H. Chen, "Interval neutrosophic sets and their application in multicriteria decision making problems," The Scientific World Journal, vol. 2014, pp. 1-15, 2014.
32. T. L. Saaty, The Analytic Hierarchy Process, New York: McGraw-Hill, 1980.
33. S. Roychowdhury and B. H. Wang, "On generalized Hamacher families of triangular operators," International Journal of Approximate Reasoning, vol. 19, no. 3-4, pp. 419-439, 1998.
34. G. Deschrijver and E. E. Kerre, "A generalization of operators on intuitionistic fuzzy sets using triangular norms and conorms," Notes Intuition Fuzzy Sets, vol. 8, no. 1, pp. 19-27, 2002.
35. F. Smarandache and L. Vladareanu, "Applications of neutrosophic logic to robotics-An introduction," in Proc. of 2011 IEEE International Conference on Granular Computing, pp. 607-612, 2011.
36. H. Hamachar, Uber logische verknunpfungenn unssharfer Aussagen und deren Zugenhorige Bewertungsfunktione, in: Trappl, Klir, Riccardi (Eds.), Progress in Cybernatics and systems research, vol. 3, Hemisphere, Washington DC, pp. 276-288, 1978.
37. Z. S. Xu, "An overview of methods for determining OWA weights," International Journal of Intelligent Systems, vol. 20, no. 8, pp. 843-865, 2005.
38. Z. L. Yue, "Deriving decision maker's weights based on distance measure for interval-valued intuitionistic fuzzy group decision making," Expert Systems with Applications, vol. 38, no. 9, pp. 11665-11670, 2011.