Sage Journals: Discover world-class research

Abstract

For the multi-attribute group decision-making problems where attribute values are the interval-valued intuitionistic fuzzy numbers, the group decision-making method based on induced generalized Einstein geometric aggregation operators is developed. Firstly, induced generalized interval-valued intuitionistic fuzzy Einstein ordered weighted geometric (I-GIVIFEOWG) aggregation operator and induced generalized interval-valued intuitionistic fuzzy Einstein hybrid weighted geometric (I-GIVIFEHWG) aggregation operator, were proposed. Some general properties such as, idempotency, commutativity, monotonicity and boundedness, were discussed and some special cases were analyzed. Furthermore, the method for multi-attribute group decision-making problems was developed, and the operational processes were illustrated in detail. The main advantage of using the proposed methods and operators is that these operators and methods give a more complete view of the problem to the decision makers. The proposed methods provide more general, more accurate and precise results. Therefore these methods play a vital role in real world problems. Finally the proposed operators have been applied to decision making problems to show the validity, practicality and effectiveness of the new approach.

Keywords

Group decision-making I-GIVIFEOWG aggregation operator I-GIVIFEHG aggregation operator some einstein operations

Get full access to this article

View all access options for this article.

References

L.A.

Zadeh , Fuzzy sets, Information Control 8 (1965), 338–353.

K.T.

Atanassov , Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986), 87–96.

K.T.

Atanassov , More on intuitionistic fuzzy sets, Fuzzy Sets and Systems 33 (1989), 37–46.

Z.S.

Xu , Intuitionistic fuzzy aggregation operators, IEEE Trans Fuzzy Syst 15 (2007), 1179–1187.

Z.S.

Xu and

R.R.

Yager , Some geometric aggregation operators based on intuitionistic fuzzy Sets, International Journal of General System 35 (2006), 417–433.

D.F.

Li ,

G.H.

Chen and

Z.G.

Huang , Linear programming method for multiattribute group decision making using IF sets, Information Sciences 180 (2010), 1591–1609.

S.P.

Wan and

D.F.

Li , Fuzzy LINMAP approach to heterogeneous MADM considering comparisons of alternatives with hesitation degrees, Omega: The International Journal of management Science 41 (2013), 925–940.

G.F.

Yu ,

Fei and

D.F.

Li , A compromise-typed variable weight decision method for hybrid multi-attribute decision making, IEEE Transactions on Fuzzy Systems 27 (2019), 861–872.

G.F.

Yu ,

D.F.

Li and

Fei , A novel method for heterogeneous multi-attribute group decision making with preference deviation, Computers & Industrial Engineering 124 (2018), 58–64.

10.

Wang and

Liu , Intuitionistic fuzzy geometric aggregation operators based on einstein operations, International Journal of Intelligent Systems 26 (2011), 1049–1075.

11.

Wang and

Liu , Intuitionistic fuzzy information aggregation using Einstein operations, IEEE Trans Fuzzy Syst 20 (2012), 923–938.

12.

Zhao and

Wei , Some intuitionistic fuzzy Einstein hybrid aggregation operators and their application to multiple attribute decision making, Knowledge Based System 37 (2013), 472–479.

13.

Rahman ,

Abdullah ,

Jamil and

M.Y.

Khan , Some generalized intuitionistic fuzzy Einstein hybrid aggregation operators and their application to multiple-attribute group decision-making, Int J Fuzzy Syst 20 (2018), 1567–1575.

14.

Xu ,

Li and

Wang , The induced intuitionistic fuzzy Einstein aggregation and its application in group decision-making, Journal of Industrial and Production Engineering 30 (2013), 2–14.

15.

K.A.

Atanassov and

Gargov , Interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems 31 (1989), 343–349.

16.

Z.S.

Xu and

Chen , Approach to group decision making based on interval-valued intuitionistic judgment matrices, Systems Engineering-Theory and Practice 27 (2007), 126–133.

17.

Z.S.

Xu and

Chen , On geometric aggregation over interval-valued intuitionistic fuzzy Information, In Proceedings of the Fourth International Conference on Fuzzy Systems and Knowledge Discovery, Washington, DC, USA: IEEE Computer Society Press, 2007, pp. 466–471.

18.

Zhao ,

Z.S.

Xu ,

M.F.

Ni and

Liu , Generalized aggregation operators for intuitionistic fuzzy sets, International Journal of Intelligent Systems 25 (2010), 1–30.

19.

Z.S.

Xu , Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making, Control and Decision 22 (2007), 215–219.

20.

D.J.

Yu ,

Y.Y.

Wu and

Lu , Interval-valued intuitionistic fuzzy prioritized operators and their application in group decision making, Knowledge-Based Systems 30 (2012), 57–66.

21.

Su ,

G.P.

Xia and

M.Y.

Chen , Some induced intuitionistic fuzzy aggregation operators applied to multi-attribute group decision making, International Journal of General Systems 40(2911), 805–835.

22.

Wei and

Wang , Some geometric aggregation operators based on interval-valued intuitionistic fuzzy sets and their application to group decision making, in: Proceedings of the IEEE International Conference on Computational Intelligence and Security, 2007, pp. 495–499.

23.

Cai and

Han , Some induced Einstein aggregation operators based on the data mining with interval-valued intuitionistic fuzzy information and their application to multiple attribute decision-making, Journal of Intelligent & Fuzzy Systems 27 (2014), 331–338.

24.

W.Z.

Wang and

X.W.

Liu , Some interval-valued intuitionistic fuzzy geometric aggregation operators based on Einstein operations, FSKD, Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2012), 2012, pp. 621–625.

25.

Yang and

Sheng , Induced interval-valued intuitionistic fuzzy Einstein ordered weighted geometric operator and their application to multiple attribute decision-making, Journal of Intelligent & Fuzzy Systems 26 (2014), 2945–2954.