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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 2931482, 20 pages
https://doi.org/10.1155/2017/2931482
Research Article

Interval-Valued Hesitant Fuzzy Multiattribute Group Decision Making Based on Improved Hamacher Aggregation Operators and Continuous Entropy

1School of Information Science & Engineering, Changzhou University, Changzhou, Jiangsu 213164, China
2School of Petroleum Engineering, Changzhou University, Changzhou, Jiangsu 213164, China

Correspondence should be addressed to Ning Zhou; nc.ude.uzcc@gninuohz

Received 2 January 2017; Revised 21 April 2017; Accepted 26 April 2017; Published 26 September 2017

Academic Editor: Peide Liu

Copyright © 2017 Jun Liu 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. K. T. Atanassov, “More on intuitionistic fuzzy sets,” Fuzzy Sets and Systems. An International Journal in Information Science and Engineering, vol. 33, no. 1, pp. 37–45, 1989. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. K. T. Atanassov, “Two theorems for intuitionistic fuzzy sets,” Fuzzy Sets and Systems. An International Journal in Information Science and Engineering, vol. 110, no. 2, pp. 267–269, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  5. R. R. Yager, “Some aspects of intuitionistic fuzzy sets,” Fuzzy Optimization and Decision Making. A Journal of Modeling and Computation Under Uncertainty, vol. 8, no. 1, pp. 67–90, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. P. Liu and F. Jin, “A multi-attribute group decision-making method based on weighted geometric aggregation operators of interval-valued trapezoidal fuzzy numbers,” Applied Mathematical Modelling. Simulation and Computation for Engineering and Environmental Systems, vol. 36, no. 6, pp. 2498–2509, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. S. Abdullah, M. Aslam, and K. Hila, “Interval valued intuitionistic fuzzy sets in Γ-semihypergroups,” International Journal of Machine Learning and Cybernetics, vol. 7, no. 2, pp. 217–228, 2016. View at Publisher · View at Google Scholar · View at Scopus
  8. M. Xia and Z. Xu, “Some new similarity measures for intuitionistic fuzzy values and their application in group decision making,” Journal of Systems Science and Systems Engineering, vol. 19, no. 4, pp. 430–452, 2010. View at Publisher · View at Google Scholar · View at Scopus
  9. K. K. Myithili, R. Parvathi, and M. Akram, “Certain types of intuitionistic fuzzy directed hypergraphs,” International Journal of Machine Learning and Cybernetics, vol. 7, no. 2, pp. 287–295, 2016. View at Publisher · View at Google Scholar · View at Scopus
  10. G. Wei, “Gray relational analysis method for intuitionistic fuzzy multiple attribute decision making,” Expert Systems with Applications, vol. 38, no. 9, pp. 11671–11677, 2011. View at Publisher · View at Google Scholar · View at Scopus
  11. M. Xia and Z. S. Xu, “Entropy/cross entropy-based group decision making under intuitionistic fuzzy environment,” Information Fusion, vol. 13, no. 1, pp. 31–47, 2012. View at Publisher · View at Google Scholar · View at Scopus
  12. B. Kang, Y. Hu, Y. Deng, and D. Zhou, “A new methodology of multicriteria decision-making in supplier selection based on Z-numbers,” Mathematical Problems in Engineering, Article ID 8475987, Art. ID 8475987, 17 pages, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  13. K. Atanassov and G. Gargov, “Interval valued intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 31, no. 3, pp. 343–349, 1989. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. V. Torra and Y. Narukawa, “On hesitant fuzzy sets and decision,” in Proceedings of the IEEE International Conference on Fuzzy Systems, pp. 1378–1382, Jeju-do, Republic of Korea, August 2009. View at Publisher · View at Google Scholar · View at Scopus
  15. V. Torra, “Hesitant fuzzy sets,” International Journal of Intelligent Systems, vol. 25, no. 6, pp. 529–539, 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. I. B. Turksen, “Interval valued fuzzy sets based on normal forms,” Fuzzy Sets and Systems, vol. 20, no. 2, pp. 191–210, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  17. N. Chen, Z. S. Xu, and M. M. Xia, “Interval-valued hesitant preference relations and their applications to group decision making,” Knowledge-Based Systems, vol. 37, pp. 528–540, 2013. View at Publisher · View at Google Scholar · View at Scopus
  18. N. Chen, Z. Xu, and M. Xia, “Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis,” Applied Mathematical Modelling. Simulation and Computation for Engineering and Environmental Systems, vol. 37, no. 4, pp. 2197–2211, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. M. Xia and Z. Xu, “Hesitant fuzzy information aggregation in decision making,” International Journal of Approximate Reasoning, vol. 52, no. 3, pp. 395–407, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. R. R. Yager and D. P. Filev, “Induced ordered weighted averaging operators,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 29, no. 2, pp. 141–150, 1999. View at Publisher · View at Google Scholar · View at Scopus
  21. J. Y. Dong and S. P. Wan, “Arithmetic aggregation operators for interval-valued intuitionistic linguistic variables and application to multi-attribute group decision making,” Iranian Journal of Fuzzy Systems, vol. 13, no. 1, pp. 1–23, 163, 2016. View at Google Scholar · View at MathSciNet · View at Scopus
  22. R. R. Yager, “On ordered weighted averaging aggregation operators in multicriteria decisionmaking,” Institute of Electrical and Electronics Engineers. Transactions on Systems, Man, and Cybernetics, vol. 18, no. 1, pp. 183–190, 1988. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. E. K. Zavadskas, J. Antucheviciene, S. H. R. Hajiagha, and S. S. Hashemi, “The interval-valued intuitionistic fuzzy MULTIMOORA method for group decision making in engineering,” Mathematical Problems in Engineering, vol. 2015, Article ID 560690, 13 pages, 2015. View at Publisher · View at Google Scholar · View at Scopus
  24. X. Liu and L. Chen, “On the properties of parametric geometric OWA operator,” International Journal of Approximate Reasoning, vol. 35, no. 2, pp. 163–178, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  25. X. Liu, “On the properties of equidifferent OWA operator,” International Journal of Approximate Reasoning, vol. 43, no. 1, pp. 90–107, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  26. P. D. Liu, L. He, and X. C. Yu, “Generalized hybrid aggregation operators based on the 2-dimension uncertain linguistic information for multiple attribute group decision making,” Group Decision and Negotiation, vol. 25, no. 1, pp. 103–126, 2016. View at Publisher · View at Google Scholar · View at Scopus
  27. Y. Chu and P. Liu, “Some two-dimensional uncertain linguistic Heronian mean operators and their application in multiple-attribute decision making,” Neural Computing and Applications, vol. 26, no. 6, pp. 1461–1480, 2015. View at Publisher · View at Google Scholar · View at Scopus
  28. 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
  29. Z. 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. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. G. Wei, X. Zhao, and R. Lin, “Some hesitant interval-valued fuzzy aggregation operators and their applications to multiple attribute decision making,” Knowledge-Based Systems, vol. 46, pp. 43–53, 2013. View at Publisher · View at Google Scholar · View at Scopus
  31. J.-Q. Zhu, F. Fu, K.-X. Yin, J.-Q. Luo, and D. Wei, “Approaches to multiple attribute decision making with hesitant interval-valued fuzzy information under correlative environment,” Journal of Intelligent & Fuzzy Systems, vol. 27, no. 2, pp. 1057–1065, 2014. View at Google Scholar · View at MathSciNet
  32. H. H. Uber, “logische verknunpfungenn unssharfer Aussagen undderen Zugenhorige Bewertungsfunktione,” in Progress in Cybernatics and Systems Research, Trappl, Klir, and Riccardi, Eds., pp. 276–288, Hemisphere, Washington, DC, 1978. View at Google Scholar
  33. C. Q. Tan, W. T. Yi, and X. H. Chen, “Hesitant fuzzy Hamacher aggregation operators for multicriteria decision making,” Applied Soft Computing, vol. 26, pp. 325–349, 2015. View at Publisher · View at Google Scholar
  34. Z. S. Xu and M. M. Xia, “Hesitant fuzzy entropy and cross-entropy and their use in multiattribute decision-making,” International Journal of Intelligent Systems, vol. 27, no. 9, pp. 799–822, 2012. View at Publisher · View at Google Scholar · View at Scopus
  35. L. A. Zadeh, “Probability measures of fuzzy events,” Journal of Mathematical Analysis and Applications, vol. 23, pp. 421–427, 1968. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  36. A. De Luca and S. Termini, “A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory,” Information and Control, vol. 20, no. 4, pp. 301–312, 1972. View at Publisher · View at Google Scholar · View at Scopus
  37. E. Szmidt and J. Kacprzyk, “Entropy for intuitionistic fuzzy sets,” Fuzzy Sets and Systems. An International Journal in Information Science and Engineering, vol. 118, no. 3, pp. 467–477, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  38. J. Ye, “Multicriteria fuzzy decision-making method using entropy weights-based correlation coefficients of interval-valued intuitionistic fuzzy sets,” Applied Mathematical Modelling. Simulation and Computation for Engineering and Environmental Systems, vol. 34, no. 12, pp. 3864–3870, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  39. C.-P. Wei, P. Wang, and Y.-Z. Zhang, “Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications,” Information Sciences. An International Journal, vol. 181, no. 19, pp. 4273–4286, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  40. Z. S. Xu and Q. L. Da, “The uncertain OWA operator,” International Journal of Intelligent Systems, vol. 17, no. 6, pp. 569–575, 2002. View at Publisher · View at Google Scholar · View at Scopus
  41. E. P. Klement and R. Mesiar, Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms, Elsevier, New York, USA, 2005.
  42. 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, pp. 78–88, 2012. View at Publisher · View at Google Scholar · View at Scopus
  43. L.-G. Li and D.-H. Peng, “Interval-valued hesitant fuzzy Hamacher synergetic weighted aggregation operators and their application to shale gas areas selection,” Mathematical Problems in Engineering, Article ID 181050, Art. ID 181050, 25 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  44. R. R. Yager, “OWA aggregation over a continuous interval argument with applications to decision making,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 34, no. 5, pp. 1952–1963, 2004. View at Publisher · View at Google Scholar · View at Scopus
  45. Z. Xu, “On consistency of the weighted geometric mean complex judgement matrix in AHP,” European Journal of Operational Research, vol. 126, no. 3, pp. 683–687, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  46. F. Jin, Z. Ni, and H. Chen, “Interval-valued hesitant fuzzy Einstein prioritized aggregation operators and their applications to multi-attribute group decision making,” Soft Computing, vol. 20, no. 5, pp. 1863–1878, 2016. View at Publisher · View at Google Scholar · View at Scopus
  47. J. Dong, D. Y. Yang, and S. P. Wan, “Trapezoidal intuitionistic fuzzy prioritized aggregation operators and application to multi-attribute decision making,” Iranian Journal of Fuzzy Systems, vol. 12, no. 4, pp. 1–32, 157, 2015. View at Google Scholar · View at MathSciNet · View at Scopus
  48. F. Jin, Z. Ni, H. Chen, and Y. Li, “Approaches to group decision making with intuitionistic fuzzy preference relations based on multiplicative consistency,” Knowledge-Based Systems, vol. 97, pp. 48–59, 2016. View at Publisher · View at Google Scholar · View at Scopus
  49. G. Z. Hu and Z. G. Zhou, “Interval-valued hesitant fuzzy entropy and its application to local higher education development research,” Computer Engineering and Applications, vol. 50, no. 23, pp. 26–30, 2014. View at Google Scholar