In recent decades, many multi-attribute decision-making methods have not been effectively applied to solve practical problems because of various shortcomings. The purpose of this paper is to develop a novel dynamic multi-attribute decision-making (DMADM) method based on the improved weights function and score function. In this paper, a novel method based on the improved entropy of interval-valued intuitionistic fuzzy sets is applied to calculate attribute weight. A time weight method is developed via the multi-target nonlinear programming model based on the ideal solution and information entropy. The influence of decision-makers’ subjective preference and objective attribute information are integrated into the time weight. A novel ranking method based on the improved score function is used to select the best alternative in the DMADM process. Moreover, the interaction among attributes is considered by the interval-valued intuitionistic fuzzy geometric weighted Heronian means operator in the proposed method. Finally, an example of partner selection with collaborative innovation is given to verify the developed approach. This study contributes to the development of DMADM theory by using improved attribute weight, time weight, and score functions, and offers us a very useful way to deal with DMADM problems in real life.
K.Atanassov and G.Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems31(3) (1989), 343–349.
2.
X.L.Zhang and Z.H.Xu, Soft computing based on maximizing consensus and fuzzy TOPSIS approach to interval-valued intuitionistic fuzzy group decision making, Applied Soft Computing26(1) (2015), 42–56.
3.
D.K.Joshi and S.Kumar, Entropy of interval-valued intuitionistic hesitant fuzzy set and its application to group decision making problems, Granular Computing1(2018), 1–15.
4.
L.A.Zadeh, Fuzzy sets, Information and Control8(3) (1965), 338–353.
5.
C.P.Wei, P.Wang and Y.Z.Zhang, Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications, Information Sciences181(19) (2011), 4273–4286.
6.
J.J.Mao, Y.Zhao and C.Ma, A new type of compositive information entropy for IVIFS and its applications, Mathematical Problems in Engineering2016 (2016), 1–13.
7.
G.Selvachandran, P.K.Maji, R.Q.Faisal and A.R.Salleh, Distance and distance induced intuitionistic entropy of generalized intuitionistic fuzzy soft sets, Applied Intelligence47(1) (2017), 132–147.
8.
J.S.Mi, Y.Leung and W.Z.Wu, An uncertainty measure in partition-based fuzzy rough sets, International Journal of General Systems34(1) (2005), 77–90.
9.
H.Y.Zhang, W.X.Zhang and C.L.Mei, Entropy of interval-valued fuzzy sets based on distance and its relationship with similarity measure, Knowledge-Based Systems22(6) (2009), 449–454.
10.
Y.J.Zhang, P.J.Ma, X.H.Su and C.P.Zhang, Multi-attribute decision making with uncertain attribute weight information in the framework of interval-valued intuitionistic fuzzy set, Acta Automatica Sinica38(2) (2012), 220–228.
11.
B.Farhadinia, A theoretical development on the entropy of interval-valued fuzzy sets based on the intuitionistic distance and its relationship with similarity measure, Knowledge-Based Systems39(2) (2013), 79–84.
12.
Q.S.Zhang, H.Y.Xing, F.C.Liu, J.Ye and P.Tang, Some new entropy measures for interval-valued intuition-istic fuzzy sets based on distances and their relationships with similarity and inclusion measures, Information Sciences283(11) (2014), 55–69.
13.
N.Zhao and Z.S.Xu, Entropy measures for interval-valued intuitionistic fuzzy information from a comparative perspective and their application to decision making, Informatica27(1) (2016), 203–228.
14.
X.H.Chen, Z.J.Dai andX.Liu, Approach to interval-valued based on entropy intuitionistic fuzzy decision making and correlation coefficient, Systems Engineering and Electronics35(10) (2013), 791–795.
15.
Y.Y.Liu, J.F.Luo, B.Wang and K.Y.Qin, A theoretical development on the entropy of interval-valued intuitionistic fuzzy soft sets based on the distance measure, International Journal ofComputational Intelligence Systems10(1) (2017), 569–592.
16.
S.Yin, Z.Yang and S.Y.Chen, Interval-intuitionistic fuzzy multiple attribute decision making based on the improved fuzzy entropy, Systems Engineering and Electronics40(5) (2018), 1079–1084.
17.
Y.J.Zhang, P.J.Ma, X.H.Su and C.P.Zhang, Entropy on interval-valued intuitionistic fuzzy sets and its application in multi-attribute decision making, Proceedings of the International Conference on Information Fusion, IEEE, 2011, pp. 1–7.
18.
J.H.Park, H.J.Cho and Y.C.Kwun, Extension of the VIKOR method to dynamic intuitionistic fuzzy multiple attribute decision making, Computers and Mathematics with Applications65(4) (2013), 731–744.
19.
Z.X.Su, G.P.Xia and M.Y.Chen, An interactive method for dynamic intuitionistic fuzzy multiattribute group decision making, Expert Systems with Applications38(12) (2011), 15286–15295.
20.
Z.S.Xu and R.R.Yager, Dynamic intuitionistic fuzzy multi-attribute decison making, International Journal of Approximate Reasoning48(1) (2008), 246–262.
21.
M.M.Gao, T.Sun, T.Y.Zhao and H.J.Dai, Approach to dynamic multiple attribute fuzzy decision making based on the interval-valued intuitionistic fuzzy entropy and time entropy, Fuzzy Systems and Mathematics30(4) (2016), 31–41.
22.
X.Z.Zhang and C.X.Zhu, Generalized precedence order method with ranking preference for multi-attribute decision making, Systems Engineering Theory and Practice33(11) (2013), 2852–2858.
23.
B.Sun and X.F.Xu, A dynamic stochastic decision-making method based on discrete time sequences, Knowledge-Based Systems105(8) (2016), 23–28.
24.
Z.L.Yang and L.C.Huang, Dynamic stochastic multiattribute decision-making that considers random variable variance characteristics under time-sequence contingency environments, Mathematical Problems in Engineering2017 (2017), 1–9.
25.
M.L.Tseng, L.Ming, K.J.Wu, L.Zhou and D.T.D.Bui, A novel approach for enhancing green supply chain management using converged interval-valued triangular fuzzy numbers-grey relation analysis, Resources Conservation and Recycling128(1) (2018), 122–133.
26.
J.Ye, Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment, Expert Systems with Applications36(3) (2009), 6899–6902.
27.
V.L.G.Nayagam, S.Muralikrishnan and G.Sivaraman, Multi-criteria decision-making method based on interval-valued intuitionistic fuzzy sets, Expert Systems with Applications38(3) (2011), 1464–1467.
28.
T.Y.Chen, A comparative analysis of score functions for multiple criteria decision making in intuitionistic fuzzy settings, Information Sciences181(17) (2011), 3652–3676.
29.
D.F.Li, The GOWA operator based approach to multiattribute decision making using intuitionistic fuzzy sets,Mathematical and Computer Modelling53(5-6) (2011), 1182–1196.
30.
J.W.Gao, H.H.Liu and Y.D.Gu, Interval-valued intuition-istic fuzzy multi-criteria decision-making method based on prospect theory, Systems Engineering Theory and Practice34(12) (2014), 3175–3181.
31.
H.Garg, A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems, Applied Soft Computing38(1) (2016), 988–999.
32.
R.Sahin, Fuzzy multicriteria decision making method based on the improved accuracy function forinterval-valued intuitionistic fuzzy sets, Soft Computing20(7) (2016), 2557–2563.
33.
H.Garg, A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem, Journal of Intelligent and Fuzzy Systems31(1) (2016), 529–540.
34.
C.Y.Wang and S.M.Chen, An improved multiattribute decision making method based on new score function of interval-valued intuitionistic fuzzy values and linear programming methodology, Information Sciences411(10) (2017), 176–184.
35.
G.Wei, Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making, Applied Soft Computing10(2) (2010), 423–431.
36.
G.W.Wei and J.M.Merigo, Methods for strategic decision-making problems with immediate probabilities in intuitionistic fuzzy setting, Scientia Iranica19(6) (2012), 1936–1946.
37.
Z.S.Xu and J.Chen, Some models for deriving the priority weights from interval fuzzy preference relations, European Journal ofOperational Research184(1) (2007), 266–280.
38.
Z.S.Xu, A method based on distance measure for interval-valued intuitionistic fuzzy group decision making, Information Sciences180(1) (2010), 181–190.
39.
G.W.Wei, X.F.Zhao and R.Lin, Some hesitant interval-valued fuzzy aggregation operators and their applications to multiple attribute decision making, Journal ofIntelligent and Fuzzy Systems24(4) (2013), 789–803.
40.
W.Z.Wang and X.W.Liu, The multi-attribute decision making method based on interval-valued intuitionistic fuzzy Einstein hybrid weighted geometric operator, Computers and Mathematics with Applications66(10) (2013), 1845–1856.
41.
P.D.Liu and H.G.Li, Multiple attribute decision-making method based on some normal neutrosophic Bonferroni mean operators, Neural Computing and Applications25(7-8) (2015), 1–16.
42.
X.Liu, Z.F.Tao, H.Y.Chen and L.G.Zhou, A new interval-valued 2-tuple linguistic Bonferroni mean operator and its application to multiattribute group decision making, International Journal of Fuzzy Systems19(1) (2017), 86–108.
43.
X.H.Zhou, J.Yao, L.Xu and Q.H.Yuan, Interval-valued intuitionistic fuzzy geometric Heronian means and its application, Systems Engineering34(4) (2016), 140–146.
44.
A.Imesija, A new sharp double inequality for generalized Heronian, harmonic and power means, Computers and Mathematics with Applications64(4) (2012), 664–671.
P.D.Liu, Z.M.Liu and X.Zhang, Some intuitionistic uncertain linguistic Heronian mean operators and their application to group decision making, Applied Mathematics and Computation230(12) (2014), 570–586.
47.
D.J.Yu and Y.Y.Wu, Interval-valued intuitionistic fuzzy Heronian mean operators and their application in multi-criteria decision making, African Journal of Business Management6(3) (2012), 4158–4168.
48.
Z.P.Tian, J.Wang, J.Q.Wang and H.Y.Zhang, Alikelihood-based qualitative flexible approach with hesitant fuzzy linguistic information, Cognitive Computation8(4) (2016), 670–683.
49.
Z.S.Xu, Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making, Control and Decision22(2) (2007), 215–219.
50.
Z.S.Xu and R.R.Yager, Dynamic intuitionistic fuzzy multi-attribute decison making, International Journal of Approximate Reasoning48(1) (2008), 246–262.
51.
M.M.Gao, T.Sun and J.J.Zhu, Interval-valued intuitionistic fuzzy multiple attribute decision-making method based on revised fuzzy entropy and new scoring function, Control and Decision31(10) (2016), 1757–1764.
