This paper investigates intuitionistic fuzzy information aggration problem with the interrelationship among the input values and the “singular point” (i.e. the input value was either too large or too small) which canot be solved by most existing aggregation operators. To accomplish this, this paper combines the geometric Heronian mean (GHM) operator with the power geometric (PG) operator under intuitionistic fuzzy environment. Then, the intuitionistic fuzzy power GHM (IFPGHM) operator and the weighted intuitionistic fuzzy power GHM (WIFPGHM) operator are presented. The new operators capture not only the correlations between the input arguments but also the relative closeness of decision making information such that they can better solve the intuitionistic fuzzy information aggregation problem with diversified connections between arguments. The desirable properties of these new extensions of GHM operator and their special cases are investigated. Finally, based on the WIFPGHM operator, we present an approach to multiple attribute decision making and illustrate that approach with a practical example.
KaurG., GargH.Multi-attribute decision-making based on Bonferroni mean operators under cubic intuitionistic fuzzy set environment, Entropy20(1) (2018), 65.
GargR., KumarR., GargS.MADM-based parametric selection and ranking of E-learning websites using fuzzy COPRAS, IEEE Transactions on Education62(1) (2018), 11–18.
4.
YuD.J., LiaoH.C.Visualization and quantitative research on intuitionistic fuzzy studies, Journal of Intelligent & Fuzzy Systems30(6) (2016), 3653–3663.
5.
GargH., AroraR.Bonferroni mean aggregation operators under intuitionistic fuzzy soft set environment and their applications to decision-making, Journal of the Operational Research Society69(11) (2018), 1711–1724.
6.
ZadehL.A.Fuzzy sets, Information & Control8(3) (1965), 338–353.
7.
AtanassovK.T.Intuitionistic fuzzy sets, Physica-Verlag HD Press, 1999.
8.
GargH., KumarK.Linguistic interval-valued Atanassov intuitionistic fuzzy sets and their applications to group decision-making problems, IEEE Transactions on Fuzzy Systems, (2019), DOI: 10.1109/TFUZZ.2019.2897961.
9.
SirbiladzeG., SikharulidzeA.Extensions of Probability Intuitionistic Fuzzy Aggregation Operators in Fuzzy MCDM/MADM, International Journal of Information Technology & Decision Making17(02) (2018), 621–655.
10.
GargH., KumarK.A novel exponential distance and its based TOPSIS method for interval-valued intuitionistic fuzzy sets using connection number of SPA theory, (2018), DOI: 10.1007/s10462-018-9668-5.
SuZ.X., XiaG.P., ChenM.Y., WangL.Induced generalized intuitionistic fuzzy OWA operator for multi-attribute group decision making, Expert Systems with Applications39(2) (2012), 1902–1910.
15.
LiaoH.C., XuZ.S.Intuitionistic Fuzzy Hybrid Weighted Aggregation Operators, International Journal of Intelligent Systems29(11) (2014), 971–993.
16.
ZengS., SuW., ZhangC.Intuitionistic fuzzy generalized probabilistic ordered weighted averaging operator and its application to group decision making, Technological and Economic Development of Economy22(2) (2015), 1–17.
17.
GargH.Intuitionistic Fuzzy Hamacher Aggregation Operators with Entropy Weight and Their Applications to Multi-criteria Decision-Making Problems, Iranian Journal of Science and Technology, Transactions of Electrical Engineering, (2019), doi: 10.1007/s40998-018-0167-0.
HanB., ChenH.Y., ZhuJ.M., LiuJ.P.An approach to linguistic multiple attribute decision-making based on unbalanced linguistic generalized heronian mean aggregation operator, Computational Intelligence and Neuroscience2018 (2018), 1–25.
20.
ZangY., ZhaoX., LiS.Interval-Valued Dual Hesitant Fuzzy Heronian Mean Aggregation Operators and their Application to Multi-Attribute Decision Making, International Journal of Computational Intelligence and Applications17(1) (2018), 1–20.
21.
PengH.G., WangJ.Q., ChengP.F.A linguistic intuitionistic multi-criteria decision-making method based on the Frank Heronian mean operator and its application in evaluating coal mine safety, International Journal of Machine Learning and Cybernetics9(6) (2018), 1053–1068.
22.
LiuP.D., ChenS.M.Group Decision Making Based on Heronian Aggregation Operators of Intuitionistic Fuzzy Numbers, IEEE Trans Cybern99 (2017), 2514–2530.
YagerR.R.The power average operator, Systems Man & Cybernetics Part A Systems & Humans IEEE Transactions on31(6) (2001), 724–731.
25.
JiangW., WeiB.Y.Intuitionistic fuzzy evidential power aggregation operator and its application in multiple criteria decision-making, International Journal of Systems Science49(3) (2018), 582–594.
26.
LiuP.D., WangP.Some interval-valued intuitionistic fuzzy Schweizer– Sklar power aggregation operators and their application to supplier selection, International Journal of Systems Science49(6) (2018), 1188–1211.
27.
JiangW., WeiB.Y., LiuX., ZhengH.Q.Intuitionistic Fuzzy Power Aggregation Operator Based on Entropy and Its Application in Decision Making, International Journal of Intelligent Systems33(1) (2018), 49–67.
28.
WanS.P., DongJ.Y.Power geometric operators of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute group decision making, Applied Soft Computing29 (2015), 153–168.
29.
XuZ.S., YagerR.R.Power-Geometric Operators and Their Use in Group Decision Making, IEEE Transactions on Fuzzy Systems18(1) (2010), 94–105.
30.
DimpleR., HarishG.Complex intuitionistic fuzzy power aggregation operators and their applications in multicriteria decision-making, Expert Systems, (2018), 10.1111/exsy.12325.
31.
WeiG.W., LuM.Pythagorean fuzzy power aggregation operators in multiple attribute decision making, International Journal of Intelligent Systems33(1) (2018), 169–186.
32.
LiuP.D., LiuX.The neutrosophic number generalized weighted power averaging operator and its application in multiple attribute group decision making, International Journal of Machine Learning and Cybernetics9(2) (2018), 347–358.
33.
JiangW., WeiB.Y., LiuX., LiX.Y., ZhengH.Q.Intuitionistic Fuzzy Power Aggregation Operator Based on Entropy and Its Application in Decision Making, Interna-tional Journal of Intelligent Systems33(1) (2018), 49–67.
34.
ShiM.H., XiaoQ.Hesitant fuzzy linguistic aggregation operators and their application to multiple attribute group decision making, Fuzzy Systems and Mathematics31(5) (2017), 68–79.
35.
HeY.D., HeZ., JinC., ChenH.Y.Intuitionistic Fuzzy Power Geometric Bonferroni Means and Their Application to Multiple Attribute Group Decision Making, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems23(2) (2015), 285–315.
36.
LiuX., TaoZ.F., ChenH.Y., ZhouL.G.A magdm method based on 2-tuple linguistic heronian mean and new operational laws, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems24(4) (2016), 593–627.
37.
SzmidtE., KacprzykJ.Amount of Information and Its Reliability in the Ranking of Atanassov’s Intuitionistic Fuzzy Alternatives// Recent Advances in Decision Making. Berlin: Springer, 2009.
38.
ZhangX.M., XuZ.S.A new method for ranking intuitionistic fuzzy values and its application in multi-attribute decision making, Fuzzy Optimization and Decision Making11(2) (2012), 135–146.
39.
JafarianE., RezvaniM.A.A valuation-based method for ranking the intuitionistic fuzzy numbers, Journal of Intelligent & Fuzzy Systems24(1) (2013), 133–144.
40.
LakshmanaG.N.V., JeevarajS., SivaramanG.Complete Ranking of Intuitionistic Fuzzy Numbers, Fuzzy Information and Engineering8(2) (2016), 237–254.
41.
ZhangZ.M.Generalized Atanassov’s intuitionistic fuzzy power geometric operators and their application to multiple attribute group decision making, Information Fusion14(4) (2013), 460–486.
42.
XiaM.M., XuZ.S., ZhuB.Geometric Bonferroni means with their application in multi-criteria decision making, Knowledge-Based Systems40 (2013), 88–100.
43.
SzmidtE., KacprzykJ.Distances between intuitionistic fuzzy sets, Fuzzy Sets and Systems114(3) (2000), 505–518.
