The aim of this paper is to investigate information aggregation methods under Pythagorean trapezoidal fuzzy environment. Pythagorean fuzzy set, an extension of the intuitionistic fuzzy set which relax the condition of sum of their membership function to square sum of its non-membership functions is less than one. In this paper, we proposed some operational rules based on PTFNs and verified their some properties. we developed some aggregation operators to use the decision information represented by PTFNS, including the Pythagorean trapezoidal fuzzy weighted averaging (PTFWA) operator, Pythagorean trapezoidal fuzzy ordered weighted averaging (PTFOWA) operator and Pythagorean trapezoidal fuzzy hybrid averaging (PTFHA) operator. Furthermore, we proved their some desirable properties. Based on the (PTFWA) operator, the PTFOWA operator and the PTFHA operator, we presented some new method to deal with the multi-attribute group decision making (MAGDM) problems under the Pythagorean trapezoidal fuzzy environment. Finally, we used some practical example to illustrate the validity and feasibility of the proposed methods by comparing with other methods.
AtanassovK.T., An equality between intuitionistic fuzzy sets, Fuzzy Sets and Systems79(2) (1996), 257–258.
4.
LiD.F., Closeness coefficient based nonlinear programming method for interval-valued intuitionistic fuzzy multiattribute decision making with incomplete preference information, Appl Soft Comput11 (2011), 3042–3418.
5.
WanS.P. and LiD.F., Fuzzy linmap approach to heterogeneous MADM considering comons of alternatives with hesitation degrees, Omega41(6) (2013), 925–940.
6.
SzmidtE. and KacprzykJ., Intuitionistic fuzzy sets in some medical applications, in Computational Intelligence. Theory and Applications, Springer, pp, (2001), 148–151.
7.
ShakeelM., Induced averaging aggregation operators with interval pythagorean trapezoidal fuzzy numbers and their application to group decision making, The Nucleus2 (2017), 140–153.
8.
WangJ.Q., Overview on fuzzy multi-criteria decision making approach, Control Decision23 (2008), 601–606.
9.
WangJ.Q. and ZhangZ., Multi-criteria decision-making method with incomplete certain information based on intuitionistic fuzzy number, Control Decision24 (2009), 226–230.
10.
WeiG.W., Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making, Appl Soft Comput10 (2010), 423–431.
11.
YagerR.R., Pythagorean fuzzy subsets. In Edmonton, Proc Joint IFSA World Congress and NAFIPS Annual MeetingCanada, (2013), pp, 57–61.
12.
XuZ.S., An overview of methods for determining owa weights, Int J Intell Syst20 (2005), 843–865.
13.
AtanassovK., New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets Syst (1994), 137–142.
14.
DeS.K., BiswasR. and RoyA.R., An application of intuitionistic fuzzy sets in medical diagnosis, Fuzzy Sets and Systems117 (2001), 209–213.
15.
ChenZ. and YangW., A new multiple attribute group decision making method in intuitionistic fuzzy setting, Applied Mathematical Modelling35 (2011), 4424–4437.
16.
KharalA., Homeopathic drug selection using intuitionistic fuzzy sets, Homeopathy98 (2009), 35–39.
17.
XuZ.S. and YagerR.R., Some geometric aggregation operators based on intuitionistic fuzzy sets, Int J Gen Syst (2006), 417–433.
18.
XuZ.S. and YagerR.R., Dynamic intuitionistic fuzzy multi-attribute decision making, Int J Approx Reason (2008), 246–262.
19.
MaZ. and XuZ., Symmetric pythagorean fuzzy weighted geometric/averaging operators and their application in multicriteria decision-making problems, International Journal of Intelligent Systems (2016), 1–22.
20.
ZhangX. and XuZ., Extension of TOPSIS to multiple criteria decision making with pythagorean fuzzy sets, International Journal of Intelligent Systems29 (2014), 1061–1078.
21.
YagerR.R., Pythagorean membership grades in multi-criteria decision making, IEEE Trans Fuzzy Syst22 (2014), 958–965.
22.
GargH., A novel improved accuracy function for interval valued Pythagorean fuzzy sets and its applications in decision making process, International Journal of Intelligent Systems, Wiley32 (2017), 1247–1260.
23.
GargH., Confidence levels based Pythagorean fuzzy aggregation operators and its application to decision-making process, Computational and Mathematical Organization Theory23 (2017), 546–571.
24.
KumarK. and GargH., TOPSIS method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environment, Computational and Applied Mathematics (2016), 1–11.
25.
GargH., A linear programming method based on an improved score function for interval-valued Pythagorean fuzzy numbers and its application to decision-making, International Journal of Uncertainties, Fuzziness and Knowledge-Based Systems26 (2018), 67–80.
26.
GargH., Generalized Pythagorean fuzzy Geometric aggregation operators using Einstein t-norm and t-conorm for multicriteria decision-making process, Intenational Journal of Intelligent Systems, Wiley32 (2017), 597–630.
27.
GargH., A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision-making processes, International Journal of Intelligent Systems, Wiley31 (2016), 1234–1253.
28.
GargH., A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem, Journal of Intelligent and Fuzzy Systems31 (2016), 529–540.
29.
GargH., A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems, Applied Soft Computing, Elsevier38 (2016), 989–999.
30.
GargH., Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein t-norm and t-conorm and their application to decision making, Computer and Industrial Engineering, Elsevier101 (2016), 53–64.
31.
GargH., Novel intuitionistic fuzzy decision making method based on an improved operation laws and its application, Engineering Applications of Artificial Intelligence, Elsevier60 (2017), 164–174.
32.
Z.S.Gou, X.J.Xu, and P.J.Ren, The properties of continuous pythagorean fuzzy information, International Journal of Intelligent Systems31 (2016), 401–424.
33.
LiuJ., ChenH., XuQ.,et al. Generalized ordered modular averaging operator and its application to group decision making,&, Systems299 (2016), 1–25.
34.
Huayou ChenL.J., L.Zhou, Z.Tao
and Y.He, On the properties of the generalized OWHA operators and their application to group decision making, Journal of Intelligent and Fuzzy Systems27 (2014), 2077–2089.
35.
LiuJ., ChenH., ZhouL.., Generalized linguistic ordered weighted hybrid logarithm averaging operators and applications to group decision making, International Journal of Uncertainty Fuzziness and Knowledge-Based Systems23 (2015), 421–442.
36.
LiuJ., LinS., ChenH. and ZhouL., The continuous Quasi-OWA operator and its application to group decision making, Group Decision and Negotiation22 (2013), 715–738.
37.
HeY., HeZ., WangG. and ChenH., Hesitant fuzzy power bonferroni means and their application to multiple attribute decision making, IEEE Transactions on Fuzzy Systems23 (2015), 1655–1668.
38.
HeY. and HeZ., Extensions of Atanassov’s intuitionistic fuzzy interaction Bonferroni means and Their Application to Multiple attribute decision making, IEEE Transactions on Fuzzy Systems24 (2016), 558–573.
39.
HeY., HeZ., LeeD.H., KimK.J., ZhangL. and YangX., Robust fuzzy programming method for MRO problems considering location effect, dispersion effect and model uncertainty, Computers and Industrial Engineering105 (2017), 76–83.
40.
HeY., HeZ. and ChenH., Intuitionistic fuzzy interaction bonferroni means and its application to multiple attribute decision making, IEEE Transactions on Cybernetics45 (2015), 116–128.
41.
A.I.Ban
and D.A.Tus’e, Trapezoidal/triangular intuitionistic fuzzy numbers versus interval-valued trapezoidal/triangular fuzzy numbers and applications to multicriteria decision making methods, Sofia, In Conf on IFSs2014, pp. 10–11.
42.
WeiG., Some arithmetic aggregation operators with intuitionistic trapezoidal fuzzy numbers and their application to group decision making, J Comput5(3) (2010), 345–351.
43.
WanS.P. and DongJ.-Y., Method of intuitionistic trapezoidal fuzzy number for multiattribute group decision, Control Decis25(5) (2010), 773–776.
44.
WuJ. and CaoQ.-W., Same families of geometric aggregation operators with intuitionistic trapezoidal fuzzy numbers, Appl Math Model37(12) (2013), 318–327.
