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Group Decision and Negotiation

, Volume 28, Issue 1, pp 197–232 | Cite as

Intuitionistic Fuzzy Interaction Hamy Mean Operators and Their Application to Multi-attribute Group Decision Making

  • Peide LiuEmail author
  • Yumei Wang
Article
  • 51 Downloads

Abstract

The Hamy mean (HM) operator, as a useful aggregation tool, is capable of capturing the correlations among multiple integrated parameters. In this paper, we expand HM operator to integrate intuitionistic fuzzy numbers (IFNs) on the basis of interaction operational rules of IFNs, and develop intuitionistic fuzzy interaction HM (IFIHM) operator and intuitionistic fuzzy weighted interaction HM (IFWIHM) operator. Moreover, we discuss some properties and particular cases of the IFIHM operator and the IFWIHM operator in detail. In addition, in real applications, there are many decision making problems with the interactions among multiple attributes, so we present a multi-attribute group decision making (MAGDM) method based on the IFWIHM operator. At the same time, the applicability and validity of the proposed MAGDM method is illustrated clearly by using an example concerning the evaluation of scenic spots. Finally, comparing with the existing approaches, the merits of the proposed MAGDM method are demonstrated, i.e., it can deal with MAGDM problems by considering the interactions among multiple attributes based on the IFWIHM operator which is a generalization of most existing operators, and it can also overcome the weaknesses existed in the traditional operational laws of IFNs.

Keywords

Intuitionistic fuzzy set Hamy mean operator IFIHM operator IFWIHM operator Multi-attribute group decision making 

Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 71771140 and 71471172), the Special Funds of Taishan Scholars Project of Shandong Province (No. ts201511045) and a Project of Shandong Province Higher Educational Science and Technology Program (Nos. J16LN25 and J17KA189).

References

  1. Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96Google Scholar
  2. Atanassov KT (1989) More on intuitionistic fuzzy sets. Fuzzy Sets Syst 33:37–46Google Scholar
  3. Atanassov KT (1994) New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets Syst 61(2):137–142Google Scholar
  4. Benayoun R, Roy B, Sussman N (1966) Manual de reference du programme electre. Note de synthese et Form 25:79Google Scholar
  5. Bonferroni C (1950) Sulle medie multiple di potenze. Bolletino Mat Italiana 5:267–270Google Scholar
  6. Brans J (1982) L’ingénièrie de la décision; Elaboration d’instruments d’aide à la décision. La méthode PROMETHEE, Québec, Canada, Presses de l’Université Laval, pp 183–214Google Scholar
  7. De SK, Biswas R, Roy A (2000a) Some operations on intuitionistic fuzzy sets. Fuzzy Sets Syst 114(3):477–484Google Scholar
  8. De SK, Biswas R, Roy A (2000b) Some operations on intuitionistic fuzzy sets in terms of evidence theory: decision making aspect. Knowl Based Syst 23(8):772–782Google Scholar
  9. Gomes LFAM, Lima MMPP (1992) TODIM: basics and application to multicriteria ranking of projects with environmental impacts. Found Comput Decis Sci 16(4):113–127Google Scholar
  10. Hara T, Uchiyama M, Takahasi SE (1998) A refinement of various mean inequalities. J Inequal Appl 2(4):387–395Google Scholar
  11. He Y, Chen H, Zhou L, Han B, Zhao Q (2014a) Generalized intuitionistic fuzzy geometric interaction operators and their application to decision making. Expert Syst 41(5):2484–2495Google Scholar
  12. He Y, Chen H, Zhou L, Liu J, Tao Z (2014b) Intuitionistic fuzzy geometric interaction averaging operators and their application to multi-criteria decision making. Inf Sci 259:142–159Google Scholar
  13. Hwang CL, Yoon K (1981) Multiple attribute decision making: methods and applications: a state-of-the-art survey. Springer, New YorkGoogle Scholar
  14. Jiang Y, Liang X, Liang H (2017) An I-TODIM method for multi-attribute decision making with interval numbers. Soft Comput 21(18):5489–5506Google Scholar
  15. Li D (2011) The GOWA operator based approach to multi-attribute decision making using intuitionistic fuzzy sets. Math Comput Model 53:1182–1196Google Scholar
  16. Li M, Wu C, Zhang L, You LN (2015) An intuitionistic fuzzy-TODIM method to solve distributor evaluation and selection problem. Int J Simul Model 14(3):511–524Google Scholar
  17. Liu P (2017) Multiple attribute group decision making method based on interval-valued intuitionistic fuzzy power Heronian aggregation operators. Comput Ind Eng 108:199–212Google Scholar
  18. Liu P, Chen SM (2017) Group decision making based on heronian aggregation operators of intuitionistic fuzzy numbers. IEEE Trans Cybern 47(9):2514–2530Google Scholar
  19. Liu P, Chen SM (2018) Multiattribute group decision making based on intuitionistic 2-tuple linguistic information. Inf Sci 1:34.  https://doi.org/10.1016/j.ins.2017.11.059 Google Scholar
  20. Liu P, Li H (2017) Interval-valued intuitionistic fuzzy power Bonferroni aggregation operators and their application to group decision making. Cogn Comput 9(4):494–512Google Scholar
  21. Liu P, Zhang X (2011) Research on the supplier selection of a supply chain based on entropy weight and improved ELECTRE-III method. Int J Prod Res 49(3):637–646Google Scholar
  22. Liu P, Chen SM, Liu J (2017) Multiple attribute group decision making based on intuitionistic fuzzy interaction partitioned Bonferroni mean operators. Inf Sci 411:98–121Google Scholar
  23. Liu P, Liu J, Merigó JM (2018) Partitioned Heronian means based on linguistic intuitionistic fuzzy numbers for dealing with multi-attribute group decision making. Appl Soft Comput 62:395–422Google Scholar
  24. Montajabiha M (2016) An extended PROMETHE II multi-criteria group decision making technique based on intuitionistic fuzzy logic for sustainable energy planning. Group Decis Negot 25(2):221–244Google Scholar
  25. Opricovic S (1998) Multi-criteria optimization of civil engineering systems. Faculty of Civil Engineering, BelgradeGoogle Scholar
  26. Peng J, Yeh W, Lai T, Hsu C (2015) The incorporation of the Taguchi and the VIKOR methods to optimize multi-response problems in intuitionistic fuzzy environments. J Chin Inst Eng 38(7):897–907Google Scholar
  27. Qin J (2017) Interval type-2 fuzzy Hamy mean operators and their application in multiple criteria decision making. Granul Comput 7:1–21Google Scholar
  28. Qin Q, Liang F, Li L (2017) A TODIM-based multi-criteria group decision making with triangular intuitionistic fuzzy numbers. Appl Soft Comput 55:93–107Google Scholar
  29. Rong L, Liu P, Chu Y (2016) Multiple attribute group decision making methods based on intuitionistic fuzzy generalized Hamacher aggregation operator. Econ Comput Econ Cybern Stud Res 50(2):211–230Google Scholar
  30. Roy B (1978) ELECTRE III: un algorithme de classement fondé sur une représentation floue des préférences en présence de critères multiples. Cahiers du CERO 20(1):3–24Google Scholar
  31. Sýkora S (2009) Mathematical means and averages: generalized heronian means. Sykora S. Stan’s Library, MilanGoogle Scholar
  32. Wang Y, Xi C, Zhang S, Zhang W, Yu D (2015) Combined approach for government E-tendering using GA and TOPSIS with intuitionistic fuzzy information. PLoS ONE 10(7):e0130767Google Scholar
  33. Wang T, Liu J, Li J, Niu C (2016) An integrating OWA–TOPSIS framework in intuitionistic fuzzy settings for multiple attribute decision making. Comput Ind Eng 98:185–194Google Scholar
  34. Wei G (2010) Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making. Appl Soft Comput 10:423–431Google Scholar
  35. Xu Z (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15(6):1179–1187Google Scholar
  36. Xu Z, Xia M (2011) Induced generalized intuitionistic fuzzy operators. Knowl Based Syst 24:197–209Google Scholar
  37. Xu Z, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gener Syst 35:417–433Google Scholar
  38. Xu Z, Yager RR (2011) Intuitionistic fuzzy Bonferroni means. IEEE Trans Syst Man Cybern B Cybern 41(2):568–578Google Scholar
  39. Yager RR (1988) On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans Syst Man Cybern 18(1):183–190Google Scholar
  40. Yager RR (2001) The power average operator. IEEE Trans Syst Man Cybern Part A Syst Hum 31:724–731Google Scholar
  41. Yager RR (2004) Generalized OWA aggregation operators. Fuzzy Optim Decis Mak 3:93–107Google Scholar
  42. Yu D (2013) Intuitionistic fuzzy geometric Heronian mean aggregation operators. Appl Soft Comput 13(2):1235–1246Google Scholar
  43. Zhang X, Liu P, Wang Y (2015) Multiple attribute group decision making methods based on intuitionistic fuzzy frank power aggregation operators. J Intell Fuzzy Syst 29(5):2235–2246Google Scholar
  44. Zhao H, Xu Z, Ni M, Liu S (2010) Generalized aggregation operators for intuitionistic fuzzy sets. Int J Intell Syst 25(1):1–30Google Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of Management Science and EngineeringShandong University of Finance and EconomicsJinanChina

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