The interval neutrosophic set (INS) can be better to express the incomplete, indeterminate and inconsistent information, and the power average (PA) operator can take all the decision arguments and their relationships into account, and the generalized weighted aggregation (GWA) operator can reflect the mentality of the decision-makers. In this paper, we combined PA and GWA operators to INS, and proposed some aggregation operators, include interval neutrosophic power generalized aggregation (INPGA) operator, interval neutrosophic power generalized weighted aggregation (INPGWA) operator and interval neutrosophic power generalized ordered weighted aggregation (INPGOWA) operator. Firstly, we presented some new operational laws for interval neutrosophic sets and studied their properties. Then we proposed INPGA, INPGWA and INPGOWA operators, and studied some properties and special cases of them. Further, we gave a decision making method based on these operators. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness, and to illustrate the influence of the parameter on decision making results in INPGWA operator.
ZadehL.A., Fuzzy sets, Information and Control8 (1965), 338–356.
2.
AtanassovK.T., Intuitionistic fuzzy sets, Fuzzy Sets and Systems20 (1986), 87–96.
3.
AtanassovK.T., More on intuitionistic fuzzy sets, Fuzzy Sets and Systems33 (1989), 37–46.
4.
AtanassovK.T. and GargovG., Interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems3 (1989), 343–349.
5.
AtanassovK.T., Operators over interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems64 (1994), 159–174.
6.
SmarandacheF., A unifying field in logics. neutrosophy: Neutrosophic probability, set and logic, American Research Press, Rehoboth, 1998.
7.
WangH.,
SmarandacheF.,
ZhangY. and
SunderramanR., Single valued neutrosophic sets, Proc Of 10th 476 Int Conf on Fuzzy Theory and Technology, Salt Lake City, 477 Utah, 2005.
8.
SmarandacheF. and VladareanuL., Applications of Neutrosophic Logic to Robotics-An Introduction, 2011 IEEE International Conference on Granular Computing, pp. 607–612.
9.
YeJ., A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets, Journal of Intelligent and Fuzzy Systems (2013). doi: 10.3233/IFS-130916
10.
YeJ., Single valued neutrosophic cross-entropy for multicriteria decision making problems, Applied Mathematical Modelling (2013). doi: 10.1016/j.apm.2013.07.020
11.
YeJ., Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment, International Journal of General Systems42(4) (2013), 386–394.
12.
WangH., SmarandacheF., ZhangY.Q., et al., Interval neutrosophic sets and logic: Theory and applications in computing, Hexis, Phoenix, AZ, 2005.
13.
YeJ., Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making, Journal of Intelligent & Fuzzy Systems (2013). doi: 10.3233/IFS-120724
14.
ChenS.M. and LeeL.W., Autocratic decision making using group recommendations based on the ILLOWA operator and likelihood-Based comparison relations, IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans42(1) (2012), 115–129.
15.
XuZ.S. and YagerR.R., Power-geometric operators and their use in group decision making, IEEE Transactions on Fuzzy Systems18(1) (2010), 94–105.
16.
BeliakovG., BustinceH., JamesS., CalvoT. and FernandezJ., Aggregation for atanassov’s intuitionistic and interval valued fuzzy sets: The median operator, IEEE Transactions on Fuzzy Systems20(3) (2012), 487–498.
17.
LiuP.D., Some Hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to Group Decision Making, IEEE Transactions on Fuzzy systems22(1) (2014), 83–97.
18.
LiuP.D., Some generalized dependent aggregation operators with intuitionistic linguistic numbers and their application to group decision making,, Journal of Computer and System Sciences79(1) (2013), 131–143.
19.
LiuP.D. and JinF., Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision making, Information Sciences205 (2012), 58–71.
20.
LiuP.D., A weighted aggregation operators multi-attribute group decision-making method based on interval-valued trapezoidal fuzzy numbers, Expert Systems With Applications38(1) (2011), 1053–1060.
21.
LiuP.D., ZhangX. and JinF., A multi-attribute group decision-making method based on interval-valued trapezoidal fuzzy numbers hybrid harmonic averaging operators, Journal of Intelligent & Fuzzy Systems23(5) (2012), 159–168.
22.
FanZ.P. and LiuY., An approach to solve group-decision-making problems with ordinal interval numbers,, IEEE Transactions on Systems Man and Cybernetics Part B-Cybernetics40(5) (2010), 1413–1423.
23.
ChenS.M. and LeeL.W., Autocratic decision making using group recommendations based on the ILLOWA operator and likelihood-based comparison relations, IEEE Transactions on Systems Man and Cybernetics Part A-Systems and Humans42(1) (2012), 115–129.
24.
YagerR.R., Weighted maximum entropy OWA aggregation with applications to decision making under risk, IEEE Transactions on Systems Man and Cybernetics Part A-Systems and Humans39(3) (2009), 555–564.
25.
XuZ.S., Multiple-attribute group decision making with different formats of preference information on attributes,, IEEE Transactions on Systems Man and Cybernetics Part B-Cybernetics37(6) (2007), 1500–1511.
26.
Herrera-ViedmaE., ChiclanaF. and HerreraF., Group decision-making model with incomplete fuzzy preference relations based on additive consistency, IEEE Transactions on Systems Man and Cybernetics Part B-Cybernetics37(1) (2007), 176–189.
27.
YagerR.R., The power average operator, IEEE Transactions on Systems Man and Cybernetics Part A-Systems and Humans31(6) (2001), 724–731.
28.
XuZ.S. and YagerR.R., Power-geometric operators and their use in group decision making, IEEE Transactions on Fuzzy Systems18(1) (2010), 94–105.
29.
XuY.J. and WangH.M., Approaches based on 2-tuple linguistic power aggregation operators for multiple attribute group decision making under linguistic environment, Applied Soft Computing11(5) (2011), 3988–3997.
30.
XuZ.S., Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators, Knowledge-Based Systems24(6) (2011), 749–760.
31.
ZhouL.G., ChenH.Y. and LiuJ.P., Generalized power aggregation operators and their applications in group decision making, Computers & Industrial Engineering62(4) (2012), 989–999.
32.
XuY.J., MerigóJ.M. and WangH.M., Linguistic power aggregation operators and their application to multiple attribute group decision making, Applied Mathematical Modelling36(11) (2012), 5427–5444.
33.
ZengS.Z., SuW.H. and ZhangC.H., Intuitionistic fuzzy generalized probabilistic ordered weighted averaging operator and its application to group decision making, Technological and Economic Development of Economy (2015). doi: 10.3846/20294913.2014.984253
