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Complexity
Volume 2017, Article ID 5937376, 16 pages
https://doi.org/10.1155/2017/5937376
Research Article

Some Generalized Pythagorean Fuzzy Bonferroni Mean Aggregation Operators with Their Application to Multiattribute Group Decision-Making

1School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China
2School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China
3Department of Industrial Engineering, Tsinghua University, Beijing 100084, China

Correspondence should be addressed to Xiaomin Zhu; nc.ude.utjb@uhzmx

Received 25 April 2017; Accepted 1 June 2017; Published 1 August 2017

Academic Editor: Jurgita Antucheviciene

Copyright © 2017 Runtong Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338–353, 1965. View at Publisher · View at Google Scholar · View at Scopus
  2. K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87–96, 1986. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. D. Yu and S. Shi, “Researching the development of Atanassov intuitionistic fuzzy set: using a citation network analysis,” Applied Soft Computing Journal, vol. 32, pp. 189–198, 2015. View at Publisher · View at Google Scholar · View at Scopus
  4. D. J. Yu and H. C. Liao, “Visualization and quantitative research on intuitionistic fuzzy studies,” Journal of Intelligent & Fuzzy Systems, vol. 30, no. 6, pp. 3653–3663, 2016. View at Google Scholar
  5. J. Mao, D. Yao, and C. Wang, “A novel cross-entropy and entropy measures of IFSs and their applications,” Knowledge-Based Systems, vol. 48, pp. 37–45, 2013. View at Publisher · View at Google Scholar · View at Scopus
  6. P. Liu and F. Teng, “Multiple criteria decision making method based on normal interval-valued intuitionistic fuzzy generalized aggregation operator,” Complexity, vol. 21, no. 5, pp. 277–290, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. V. Lakshmana, S. Jeevaraj, and G. Sivaraman, “Total ordering for intuitionistic fuzzy numbers,” Complexity, vol. 21, no. S2, pp. 54–66, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  8. V. Lakshmana, S. Jeevaraj, and P. Dhanasekaran, “A new ranking principle for ordering trapezoidal intuitionistic fuzzy numbers,” Complexity, Art. ID 3049041, 24 pages, 2017. View at Publisher · View at Google Scholar · View at MathSciNet
  9. P. Liu and X. Liu, “Multiattribute group decision making methods based on linguistic intuitionistic fuzzy power Bonferroni mean operators,” Complexity, Art. ID 3571459, 15 pages, 2017. View at Publisher · View at Google Scholar · View at MathSciNet
  10. D. Liu, X. Chen, and D. Peng, “Interval-valued intuitionistic fuzzy ordered weighted cosine similarity measure and its application in investment decision-making,” Complexity, Art. ID 1891923, 11 pages, 2017. View at Publisher · View at Google Scholar · View at MathSciNet
  11. P. D. Liu, “Some Hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group decision making,” IEEE Transactions on Fuzzy Systems, vol. 22, no. 1, pp. 83–97, 2014. View at Publisher · View at Google Scholar
  12. F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic, Neutrosophy, Neutrosophic Set, Neutrosophic Probability, American Research Press, Rehoboth, DE, USA, Third edition, 1999. View at MathSciNet
  13. P. D. Liu, Y. C. Chu, Y. W. Li, and Y. B. Chen, “Some generalized neutrosophic number hamacher aggregation operators and their application to group decision making,” International Journal of Fuzzy Systems, vol. 16, no. 2, pp. 242–255, 2014. View at Google Scholar · View at Scopus
  14. P. D. Liu and G. L. Tang, “Some power generalized aggregation operators based on the interval neutrosophic sets and their application to decision making,” Journal of Intelligent Fuzzy Systems, vol. 30, no. 5, pp. 2517–2528, 2016. View at Google Scholar
  15. P. Liu and H. Li, “Multiple attribute decision-making method based on some normal neutrosophic Bonferroni mean operators,” Neural Computing and Applications, 2016. View at Publisher · View at Google Scholar · View at Scopus
  16. P. Liu and G. Tang, “Multi-criteria Group Decision-Making Based on Interval Neutrosophic Uncertain Linguistic Variables and Choquet Integral,” Cognitive Computation, vol. 8, no. 6, pp. 1036–1056, 2016. View at Publisher · View at Google Scholar · View at Scopus
  17. P. D. Liu, L. L. Zhang, X. Liu, and P. Wang, “Multi-valued neutrosophic number Bonferroni mean operators with their applications in multiple attribute group decision making,” International Journal of Information Technology & Decision Making, vol. 15, no. 5, pp. 1181–1210, 2016. View at Google Scholar
  18. P. Liu, “The Aggregation Operators Based on Archimedean t-Conorm and t-Norm for Single-Valued Neutrosophic Numbers and their Application to Decision Making,” International Journal of Fuzzy Systems, vol. 18, no. 5, pp. 849–863, 2016. View at Publisher · View at Google Scholar · View at Scopus
  19. R. R. Yager, “Pythagorean membership grades in multicriteria decision making,” IEEE Transactions on Fuzzy Systems, vol. 22, no. 4, pp. 958–965, 2014. View at Publisher · View at Google Scholar · View at Scopus
  20. X. Gou, Z. Xu, and P. Ren, “The Properties of Continuous Pythagorean Fuzzy Information,” International Journal of Intelligent Systems, vol. 31, no. 5, pp. 401–424, 2016. View at Publisher · View at Google Scholar · View at Scopus
  21. X. L. Zhang and Z. S. Xu, “Extension of TOPSIS to multiple criteria decision making with pythagorean fuzzy sets,” International Journal of Intelligent Systems, vol. 29, no. 12, pp. 1061–1078, 2014. View at Publisher · View at Google Scholar · View at Scopus
  22. D. Yu, “A scientometrics review on aggregation operator research,” Scientometrics, vol. 105, no. 1, pp. 115–133, 2015. View at Publisher · View at Google Scholar · View at Scopus
  23. R. R. Yager and A. M. Abbasov, “Pythagorean membership grades, complex numbers, and decision making,” International Journal of Intelligent Systems, vol. 28, no. 5, pp. 436–452, 2013. View at Publisher · View at Google Scholar · View at Scopus
  24. Z. Ma and Z. Xu, “Symmetric Pythagorean Fuzzy Weighted Geometric/Averaging Operators and Their Application in Multicriteria Decision-Making Problems,” International Journal of Intelligent Systems, vol. 31, no. 12, pp. 1198–1219, 2016. View at Publisher · View at Google Scholar · View at Scopus
  25. S. Z. Zeng, J. P. Chen, and X. S. Li, “A hybrid method for Pythagorean fuzzy multiple-criteria decision making,” International Journal of Information Technology & Decision Making, vol. 15, no. 2, pp. 403–422, 2016. View at Google Scholar
  26. H. Garg, “A New Generalized Pythagorean Fuzzy Information Aggregation Using Einstein Operations and Its Application to Decision Making,” International Journal of Intelligent Systems, vol. 31, no. 9, pp. 886–920, 2016. View at Publisher · View at Google Scholar · View at Scopus
  27. X. Peng and H. Yuan, “Fundamental properties of Pythagorean fuzzy aggregation operators,” Fundamenta Informaticae, vol. 147, no. 4, pp. 415–446, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  28. X. D. Peng and Y. Yang, “Pythagorean fuzzy choquet integral based MABAC method for multiple attribute group decision making,” International Journal of Intelligent Systems, vol. 31, no. 10, pp. 989–1020, 2016. View at Publisher · View at Google Scholar · View at Scopus
  29. C. Bonferroni, “Sulle medie multiple di potenze,” Bolletino Matematica Italiana, vol. 5, pp. 267–270, 1950. View at Google Scholar · View at MathSciNet
  30. S. Sykora, Mathematical Means and Averages: Generalized Heronian Means, Library, SykoraS. Stans, 2009.
  31. Z. S. Xu and R. R. Yager, “Intuitionistic fuzzy bonferroni means,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 41, no. 2, pp. 568–578, 2011. View at Publisher · View at Google Scholar · View at Scopus
  32. M. Xia, Z. Xu, and B. Zhu, “Geometric Bonferroni means with their application in multi-criteria decision making,” Knowledge-Based Systems, vol. 40, pp. 88–100, 2013. View at Publisher · View at Google Scholar · View at Scopus
  33. D. J. Yu, “Intuitionistic fuzzy geometric Heronian mean aggregation operators,” Applied Soft Computing Journal, vol. 13, no. 2, pp. 1235–1246, 2013. View at Publisher · View at Google Scholar · View at Scopus
  34. B. Zhu and Z. S. Xu, “Hesitant fuzzy Bonferroni means for multi-criteria decision making,” Journal of the Operational Research Society, vol. 64, no. 12, pp. 1831–1840, 2013. View at Publisher · View at Google Scholar · View at Scopus
  35. B. Zhu, Z. Xu, and M. Xia, “Hesitant fuzzy geometric Bonferroni means,” Information Sciences. An International Journal, vol. 205, pp. 72–85, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  36. D. Yu, “Hesitant fuzzy multi-criteria decision making methods based on Heronian mean,” Technological and Economic Development of Economy, 2015. View at Publisher · View at Google Scholar · View at Scopus
  37. G. Beliakov, S. James, T. Rückschlossová, and R. R. Yager, “Generalized Bonferroni mean operators in multi-criteria aggregation,” Fuzzy Sets and Systems. An International Journal in Information Science and Engineering, vol. 161, no. 17, pp. 2227–2242, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  38. M. Xia, Z. Xu, and B. Zhu, “Generalized intuitionistic fuzzy Bonferroni means,” International Journal of Intelligent Systems, vol. 27, no. 1, pp. 23–47, 2012. View at Publisher · View at Google Scholar · View at Scopus
  39. Z. Xu, “Intuitionistic fuzzy aggregation operators,” IEEE Transactions on Fuzzy Systems, vol. 15, no. 6, pp. 1179–1187, 2007. View at Publisher · View at Google Scholar · View at Scopus
  40. Z. S. Xu and H. Hu, “Projection models for intuitionistic fuzzy multiple attribute decision making,” International Journal of Information Technology & Decision Making, vol. 9, no. 2, pp. 267–280, 2010. View at Publisher · View at Google Scholar