Skip to main content
Top

2015 | OriginalPaper | Chapter

Multiple Attribute Group Decision Making Under Hesitant Fuzzy Environment

Authors : Weize Wang , Qi-An Lu, Li Yang

Published in: Outlooks and Insights on Group Decision and Negotiation

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

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.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Yager, R.R., Kacprzyk, J.: The Ordered Weighted Averaging Operator: Theory and Applications. Kluwer, Boston (1997)CrossRef Yager, R.R., Kacprzyk, J.: The Ordered Weighted Averaging Operator: Theory and Applications. Kluwer, Boston (1997)CrossRef
2.
go back to reference Calvo, T., Mayor, G., Mesiar, R.: Aggregation Operators: New Trends and Applications. Physica-Verlag, Heidelberg (2002)CrossRef Calvo, T., Mayor, G., Mesiar, R.: Aggregation Operators: New Trends and Applications. Physica-Verlag, Heidelberg (2002)CrossRef
3.
go back to reference Xu, Z.S., Da, Q.L.: An overview of operators for aggregating information. Int. J. Intell. Syst. 18(9), 953–969 (2003)CrossRef Xu, Z.S., Da, Q.L.: An overview of operators for aggregating information. Int. J. Intell. Syst. 18(9), 953–969 (2003)CrossRef
4.
go back to reference Torra, V., Narukawa, Y.: Modeling Decisions: Information Fusion and Aggregation Operators. Springer, Berlin (2007) Torra, V., Narukawa, Y.: Modeling Decisions: Information Fusion and Aggregation Operators. Springer, Berlin (2007)
5.
go back to reference Harsanyi, J.C.: Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility. J. Polit. Econ. 63(4), 309–321 (1955)CrossRef Harsanyi, J.C.: Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility. J. Polit. Econ. 63(4), 309–321 (1955)CrossRef
6.
go back to reference Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decision-making. IEEE Trans. Syst. Man Cybern. Cybern. 18(1), 183–190 (1988)CrossRef Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decision-making. IEEE Trans. Syst. Man Cybern. Cybern. 18(1), 183–190 (1988)CrossRef
7.
go back to reference Torra, V.: The weighted OWA operator. Int. J. Intell. Syst. 12(2), 153–166 (1997)CrossRef Torra, V.: The weighted OWA operator. Int. J. Intell. Syst. 12(2), 153–166 (1997)CrossRef
9.
go back to reference Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)CrossRef Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)CrossRef
10.
go back to reference 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)CrossRef 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)CrossRef
11.
go back to reference Mizumoto, M., Tanaka, K.: Some properties of fuzzy sets of type 2. Inf. Control 31(4), 312–340 (1976)CrossRef Mizumoto, M., Tanaka, K.: Some properties of fuzzy sets of type 2. Inf. Control 31(4), 312–340 (1976)CrossRef
12.
go back to reference Dubois, D., Prade, H.M.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York (1980) Dubois, D., Prade, H.M.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York (1980)
13.
go back to reference Yager, R.R.: On the theory of bags. Int. J. Gen. Syst. 13(1), 23–37 (1986)CrossRef Yager, R.R.: On the theory of bags. Int. J. Gen. Syst. 13(1), 23–37 (1986)CrossRef
14.
go back to reference Chakrabarty, K., Despi, I.: \(n^k\)-bags. Int. J. Intell. Syst. 22(2), 223–236 (2007)CrossRef Chakrabarty, K., Despi, I.: \(n^k\)-bags. Int. J. Intell. Syst. 22(2), 223–236 (2007)CrossRef
15.
go back to reference Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25(6), 529–539 (2010) Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25(6), 529–539 (2010)
16.
go back to reference Atanassov, K., Gargov, G.: Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 31(3), 343–349 (1989)CrossRef Atanassov, K., Gargov, G.: Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 31(3), 343–349 (1989)CrossRef
17.
go back to reference 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)CrossRef 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)CrossRef
18.
go back to reference 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)CrossRef 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)CrossRef
19.
go back to reference Xia, M., Xu, Z.S.: Hesitant fuzzy information aggregation in decision making. Int. J. Approx. Reason. 52(3), 395–407 (2011)CrossRef Xia, M., Xu, Z.S.: Hesitant fuzzy information aggregation in decision making. Int. J. Approx. Reason. 52(3), 395–407 (2011)CrossRef
20.
go back to reference Torra, V., Narukawa, Y.: On hesitant fuzzy sets and decision. In: IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2009, pp. 1378–1382 (2009) Torra, V., Narukawa, Y.: On hesitant fuzzy sets and decision. In: IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2009, pp. 1378–1382 (2009)
21.
go back to reference Xu, Z.S.: Hesitant Fuzzy Sets Theory. Springer International Publishing, Heidelberg (2014)CrossRef Xu, Z.S.: Hesitant Fuzzy Sets Theory. Springer International Publishing, Heidelberg (2014)CrossRef
22.
go back to reference Xu, Z.S.: Intuitionistic fuzzy aggregation operators. IEEE Trans. Fuzzy Syst. 15(6), 1179–1187 (2007)CrossRef Xu, Z.S.: Intuitionistic fuzzy aggregation operators. IEEE Trans. Fuzzy Syst. 15(6), 1179–1187 (2007)CrossRef
23.
go back to reference Xu, Z.S., Yager, R.R.: Some geometric aggregation operators based on intuitionistic fuzzy sets. Int. J. Gen. Syst. 35(4), 417–433 (2006)CrossRef Xu, Z.S., Yager, R.R.: Some geometric aggregation operators based on intuitionistic fuzzy sets. Int. J. Gen. Syst. 35(4), 417–433 (2006)CrossRef
24.
go back to reference 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)CrossRef 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)CrossRef
25.
go back to reference Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. North Holland, New York (1983) Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. North Holland, New York (1983)
26.
go back to reference H\(\acute{a}\)jek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht (1998) H\(\acute{a}\)jek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht (1998)
Metadata
Title
Multiple Attribute Group Decision Making Under Hesitant Fuzzy Environment
Authors
Weize Wang
Qi-An Lu
Li Yang
Copyright Year
2015
DOI
https://doi.org/10.1007/978-3-319-19515-5_14

Premium Partner