In the paper, we develop the intuitionistic fuzzy induced ordered entropic weighted averaging (IFIOEWA)operator for multiple attribute group decision making (MAGDM) problems. The new operator’s attribute values take the form of intuitionistic fuzzy numbers (IFNs) and the intuitionistic fuzzy entropy (IFE) is fully taken into account, after the intuitionistic fuzzy entropic weighted averaging (IFEWA)operator is proposed. Afterwards, the prime properties of the IFIOEWA operator are investigated under some operational laws of intuitionistic fuzzy numbers (IFNs). Moreover, a method based on the IFIOEWA operator for decision-making is presented. Eventually, a numerical example is constructed to reveal the availability and applicability of the raised operator.
LucaA.D. and TerminiS., A definition of non-probabilistic entropy in the setting of fuzzy sets theory, Information and Control20 (1972), 301–312.
2.
HwangC.L. and YoonK., Multiple attribute decision making, Lecture Notes in Economics and Mathematical Systems, Springer Verlag, New York, 1981.
3.
SzmidtE. and KacprzykJ., Entropy for intuitionistic fuzzy sets, Fuzzy Sets and Systems118 (2001), 467–477.
4.
SzmidtE. and KacprzykJ., New measures of entropy for intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets11 (2005), 12–20.
5.
WeiG.W., FIOWHM operator and its application to multiple attribute group decision making, Expert Systems with Applications38(4) (2011), 2984–2989.
6.
WeiG.W., Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making, Applied Soft Computing Journal10(2) (2010), 423–431.
7.
WeiG.W., ZhaoX.F. and LinR., Some induced aggregating operators with fuzzy number intuitionistic fuzzy information and their applications to group decision making, International Journal of Computational Intelligence Systems3(1) (2010), 84–95.
8.
MerigóJ.M., A unified model between the weighted average and the induced OWA operator, Expert Systems with Applications38(9) (2011), 11560–11572.
9.
MerigóJ.M. and Gil-LafuenteA.M., Decision making techniques with similarity measures and OWA operators, Statistics and Operations Research Transactions1(1) (2012), 81–102.
10.
MerigóJ.M. and CasanovasM., Fuzzy generalized hybrid aggregation operators and its application in fuzzy decision making, International Journal of Fuzzy Systems12(1) (2010), 15–24.
11.
MerigóJ.M. and Peris-OrtizM., Palacios-MarquésD., Entrepreneurial fuzzy group decision-making under complex environments, Journal of Intelligent and Fuzzy Systems27 (2014), 901–912.
12.
AtanassovK., Intuitionistic fuzzy sets, Fuzzy Sets and Systems20 (1986), 87–96.
13.
ZadehL.A., Fuzzy sets and systems, in: Proceeding of the Symposium on Systems Theory, Polytechnic Institute of Brooklyn, New York, 1965, pp. 29–37
.
14.
ZadehL.A., Fuzzy sets, Information and Control8 (1965), 338–353.
15.
HigashiM. and KlirG., On measures of fuzziness and fuzzy complements, International Journal of General System8 (1982), 169–180.
16.
BurilloP. and BustinceH., Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy Sets and Systems78(3) (1996), 305–316.
17.
RodròguezR.M., MartinezL. and HerreraF., Hesitant fuzzy linguistic term sets for decision making, IEEE Transactions on IFIOEWA 9 Fuzzy Systems20(1) (2012), 109–119.
18.
YagerR.R., Families of OWA operators, Fuzzy Sets and System59(2) (1993), 25–148.
19.
YagerR.R., Induced aggregation operators, Fuzzy Sets and Systems137(1) (2003), 59–69.
20.
YagerR.R., Including importances in OWA aggregations using fuzzy systems modeling, IEEE Transactions on Fuzzy Systems6(2) (1998), 286–294.
21.
YagerR.R., On the measure of fuzziness and negation, part 1: Membership in the unit interval, International Journal of General System5 (1979), 221–229.
22.
YagerR.R., On ordered weighted averaging aggregation operators in multi-criteria decision making, IEEE Transactions on Systems, Man and Cybernetics B18 (1988), 183–190.
23.
YagerR.R. and FilevD.P., Induced ordered weighted averaging operators, IEEE Transactions on Systems, Man, and Cybernetics Part B29 (1999), 141–150.
24.
YagerR.R. and FilevD.P., Operations for granular computing: Mixing words and numbers, IEEE World Congress on IEEE International Conference on Fuzzy Systems1 (1998), 123–128.
25.
YagerR.R., RonaldR., KacprzykJ. and BeliakovG., Recent developments in the ordered weighted averaging operators: Theory and practice, Springer Verlag, Berlin, 2011.
26.
XianS.D., Fuzzy linguistic induced ordered weighted averaging operator and its application, Journal of Applied Mathematics2012 (2012). doi: 10.1155/2012-210392
27.
XianS.D., ZhangJ.F., XueW.T., Fuzzy linguistic induced generalized OWA operator and its application in fuzzy linguistic decision making, International Journal of Intelligent Systems2015 (2015), 1–15. doi: 10.1002/int21801
28.
XianS.D. and SunW.J., Fuzzy linguistic induced Euclidean OWA distance operator and its application in group linguistic decision making, International Journal of Intelligent Systems29(5) (2014), 478–491.
29.
XianS.D., SunW.J., XuS.H. and GaoY.Y., Fuzzy linguistic induced OWA Minkowski distance operator and its application in group decision making, Pattern Analysis and Applications17(3) (2014). doi: 10.1007/s10044-014-0397-3
30.
XianS.D., XueW.T., ZhangJ.F., YinY.B. and XieQ., Intuitionistic fuzzy linguistic induced ordered weighted averaging operator for group decision making, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems23(4) (2015), 627–648.
31.
XianS.D., XueW.T. and JingN., Fuzzy entropic ordered weighted averaging operator and its application in group decision making, International Journal of Intelligent Systems2016 (2016), 1–14. doi: 10.1002/int21808
32.
ZengS.Z., WangQ.F., MerigòJ.M. and PanT.J., Induced intuitionistic fuzzy ordered weighted averaging weighted average operator and its application to business decisionmaking, Computer Science and Information Systems11(2) (2014), 839–857.
33.
TorraV., The weighted OWA operator, International Journal of Intelligent Systems12(2) (1997), 153–166.
34.
SuW.H., YangY., ZhangC.H. and ZengS.Z., Intuitionistic fuzzy decsion-making with aimilarity measures and OWAoperators, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems21(2) (2013), 245–262.
35.
XuZ.S., Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making, Control and Decision22(2) (2007), 215–219.
36.
XuZ.S. and ChenJ., An approach to group decision making based on interval-valued intuitionistic judgment matrices, System Engineering Theory and Practice27(4) (2007), 126–133.
37.
XuZ.S. and DaQ.L., An overview of operators for aggregating information, International Journal of Intelligent Systems18(18) (2003), 953–969.
38.
XuZ.S. and YagerR.R., Some geometric aggregation operators based on intuitionistic fuzzy sets, International Journal of General Systems35(4) (2006), 417–433.
