# Multiple Attribute Group Decision Making Under Hesitant Fuzzy Environment

Conference paper
Part of the Lecture Notes in Business Information Processing book series (LNBIP, volume 218)

## Abstract

Hesitant fuzzy set is a very useful means to depict the decision information in the process of decision making. In this paper, motivated by the extension principle of hesitant fuzzy sets, we export Einstein operations on fuzzy sets to hesitant fuzzy sets, and develop some new arithmetic averaging aggregation operators, such as the hesitant fuzzy Einstein weighted averaging ($$\mathrm{{HFW}}{\mathrm{{A}}^\varepsilon }$$) operator, hesitant fuzzy Einstein ordered weighted averaging ($$\mathrm{{HFOW}}{\mathrm{{A}}^\varepsilon }$$) operator, and hesitant fuzzy Einstein hybrid weighted averaging ($$\mathrm{{HFHW}}{\mathrm{{A}}^\varepsilon }$$) operator, for aggregating hesitant fuzzy elements. Finally, we apply the proposed operators to multiple attribute group decision making with hesitant fuzzy information.

## Keywords

Hesitant fuzzy set Einstein operation Hesitant fuzzy Einstein arithmetic averaging operator Multiple attribute group decision making (MAGDM)

## Notes

### Acknowledgements

This work is supported by Natural Science Foundation of Guangxi Province (2014jjAA10065), Scientific Research Foundation of Higher Education of Guangxi Province (KY2015YB050) and the 2014 Doctoral Scientific Research Foundation of Guangxi Normal University.

## References

1. 1.
Yager, R.R., Kacprzyk, J.: The Ordered Weighted Averaging Operator: Theory and Applications. Kluwer, Boston (1997)
2. 2.
Calvo, T., Mayor, G., Mesiar, R.: Aggregation Operators: New Trends and Applications. Physica-Verlag, Heidelberg (2002)
3. 3.
Xu, Z.S., Da, Q.L.: An overview of operators for aggregating information. Int. J. Intell. Syst. 18(9), 953–969 (2003)
4. 4.
Torra, V., Narukawa, Y.: Modeling Decisions: Information Fusion and Aggregation Operators. Springer, Berlin (2007)Google Scholar
5. 5.
Harsanyi, J.C.: Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility. J. Polit. Econ. 63(4), 309–321 (1955)
6. 6.
Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decision-making. IEEE Trans. Syst. Man Cybern. Cybern. 18(1), 183–190 (1988)
7. 7.
Torra, V.: The weighted OWA operator. Int. J. Intell. Syst. 12(2), 153–166 (1997)
8. 8.
Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)
9. 9.
Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)
10. 10.
Zadeh, L.A.: Outline of a new approach to analysis of complex systems and decision processes interval-valued fuzzy sets. IEEE Trans. Syst. Man Cybern. SMC 3(1), 28–44 (1973)
11. 11.
Mizumoto, M., Tanaka, K.: Some properties of fuzzy sets of type 2. Inf. Control 31(4), 312–340 (1976)
12. 12.
Dubois, D., Prade, H.M.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York (1980)Google Scholar
13. 13.
Yager, R.R.: On the theory of bags. Int. J. Gen. Syst. 13(1), 23–37 (1986)
14. 14.
Chakrabarty, K., Despi, I.: $$n^k$$-bags. Int. J. Intell. Syst. 22(2), 223–236 (2007)
15. 15.
Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25(6), 529–539 (2010)Google Scholar
16. 16.
Atanassov, K., Gargov, G.: Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 31(3), 343–349 (1989)
17. 17.
Cornelis, C., Deschrijver, G., Kerre, E.E.: Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: construction, classification, application. Int. J. Approx. Reason. 35(1), 55–95 (2004)
18. 18.
Dubois, D., Gottwald, S., Hajek, P., Kacprzyk, J., Prade, H.: Terminological difficulties in fuzzy set theory - the case of “intuitionistic fuzzy sets”. Fuzzy Sets Syst. 156(3), 485–491 (2005)
19. 19.
Xia, M., Xu, Z.S.: Hesitant fuzzy information aggregation in decision making. Int. J. Approx. Reason. 52(3), 395–407 (2011)
20. 20.
Torra, V., Narukawa, Y.: On hesitant fuzzy sets and decision. In: IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2009, pp. 1378–1382 (2009)Google Scholar
21. 21.
Xu, Z.S.: Hesitant Fuzzy Sets Theory. Springer International Publishing, Heidelberg (2014)
22. 22.
Xu, Z.S.: Intuitionistic fuzzy aggregation operators. IEEE Trans. Fuzzy Syst. 15(6), 1179–1187 (2007)
23. 23.
Xu, Z.S., Yager, R.R.: Some geometric aggregation operators based on intuitionistic fuzzy sets. Int. J. Gen. Syst. 35(4), 417–433 (2006)
24. 24.
Zhao, H., Xu, Z.S., Ni, M., Liu, S.: Generalized aggregation operators for intuitionistic fuzzy sets. Int. J. Intell. Syst. 25(1), 1–30 (2010)
25. 25.
Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. North Holland, New York (1983)Google Scholar
26. 26.
H$$\acute{a}$$jek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht (1998)Google Scholar