Over the last decade, a lot of attentions have been drawn in the problem of multiple attribute decision-making associated with incomplete information tables. The filling missing value method and minimum decision cost are two important challenges for incomplete information tables. But most published studies focus on the optimization of data reckoning without considering the risk appetite of decision makers and decision-making environments. In this paper, considering the above factors, we presented an attribute weight determination method and an effective computing method for dealing with intuitionistic fuzzy incomplete information tables. Then, delay-refused decision in the boundary region and the risk assessment based on cross-entropy were proposed. Finally, a secondary decision strategy based on the probability entropy of delay-accepted decision and the application algorithms were given for improving the quality of decisions.
ZadehL.A., Fuzzy sets, Information & Control8(65) (1965), 338–353.
2.
AbdullahL. and NajibL., A new type-2 fuzzy set of linguistic variables for the fuzzy analytic hierarchy process, Expert Systems with Applications41(7) (2014), 3297–3305.
3.
MesiarR. and StupnanovaA., Open problems from the 12th international conference on fuzzy set theory and its applications, Fuzzy Sets and Systems261 (2015), 112–123.
4.
WangW.N. and LiuX.D., Fuzzy forecasting based on automatic clustering and axiomatic fuzzy set classification, Information Sciences294 (2015), 78–94. (In Chinese).
5.
AtanassovK.T., Intuitionistic fuzzy sets, Fuzzy Sets and Systems20(1) (1986), 87–96.
6.
AtanassovK.T., Intuitionistic fuzzy sets. New York: Physica-Verlag, Heidelberg, 1999.
7.
DeliI. and CagmanN., Intuitionistic fuzzy parameterized soft set theory and its decision making, Applied Soft Computing28 (2015), 109–113.
8.
De MiguelL., BustinceH., FernandezJ., et al., Construction of admissible linear orders for interval-valued Atanassov intuitionistic fuzzy sets with an application to decision making, Information Fusion27 (2016), 189–197.
9.
YuD.J. and ShiS.S., Researching the development of Atanassov intuitionistic fuzzy set: Using a citation network analysis, Applied Soft Computing32 (2015), 189–198. (In Chinese).
10.
PawlakZ., Rough sets, International Journal of Computer & Information Sciences11(5) (1982), 341–356.
11.
MiaoD.Q. and LiG.D., The algorithms and applications of Rough set theory. Beijing: Tsinghua University Press, 2008, pp. 1–23. (In Chinese)
12.
SleD. and ZiarkoW., The investigation of the Bayesian rough set model, International Journal of Approximate Reasoning40(1) (2005), 81–91.
13.
ZiarkoW., Variable precision rough set model, Journal of Computer and System Sciences46(1) (1993), 39–59.
14.
YaoY.Y., Probabilistic rough set approximations, International Journal of Approximate Reasoning49(2) (2008), 255–271.
15.
YaoY.Y. and WongS.K.M., A decision-theoretic rough set model, In: Proceedings of the 5th International Symposium on Methodologies for Intelligent System, Knoxville, Tennessee, 1990.
16.
YaoY.Y., Three-Way Decision: An interpretation of rules in rough set theory, In: International Conference on Rough Sets and Knowledge Technology, Springer-Verlag, 2009, pp. 642–649.
17.
YaoY.Y., Three-way decisions with probabilistic rough sets, Information Sciences180(3) (2010), 341–353.
18.
LiuD., LiT.R. and LiangD.C., Three-way decisions in dynamic decision-theoretic rough sets, In: International Conference on Rough Sets and Knowledge Technology, SpringerBerlin Heidelberg, 2013, pp. 291–301.
19.
YuH., WangG.Y., LiT.Y., et al., Three-way decisions: Methods and practices for complex problem solving. Beijing: Science Press, 2015, pp. 269–285. (In Chinese).
20.
XueZ.A., ZhuT.L., XueT.Y., et al., Three-way decisions model based on intuitionistic fuzzy sets, Computer Science43(6) (2016), 285–288,297. (In Chinese).
21.
ZhangN., DengD.Y. and PeiM.H., A model of three-way decision based on F-rough sets, Journal of NanJing University: Natural Sciences49(5) (2013), 582–587. (In Chinese).
22.
JiaX.Y., LiW.W., ShangL., et al., An adaptive learning parameters algorithm in Three-Way Decision theoretic rough set model, Acta Elfctronica Sinica39(6) (2013), 2520–2525. (In Chinese).
23.
ZhangY.J., MiaoD.Q., XuJ.F., et al., Determining thresholds in Three-way decisions: A multi-object optimization view, International Joint Conference on Rough Sets, Springer, Cham, 2017, pp. 326–339.
24.
ZhuY.H., TianH.L., ZhangY.P., et al., Adaptive algorithm for learning optimal threshold in three-way decisions based on two factors, Journal of Chinese Computer Systems37(6) (2016), 1303–1307. (In Chinese).
25.
ZhangY.P., ZouH.J. and ZhaoS., Cost sensitive three-way decisions model based on CCA, Journal of NanJing University: Natural Sciences51(2) (2015), 447–452. (In Chinese).
26.
ZhouB., YaoY.Y. and LuoJ.G., A Three-way decision approach to email spam filtering, In: Proceedings of the Advances in Artificial Intelligence, Canadian Conference on Artificial Intelligence, Canadian, Canada: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG., 2010, pp. 28–39.
27.
AyadR.A. and LiuJ., Supporting E-learning system with modified Bayesian rough set model, In: Proceedings of the 6th International Symposium on Neural Networks 2009, Lecture Notes in Computer Science 5552, Berlin: Springer, 2009, pp. 192–200.
28.
LiangD.C., WitoldP., LiuD., et al., Three-way decisions based on decision-theoretic rough sets under linguistic assessment with the aid of group decision making, Applied Soft Computing29 (2015), 256–269. (In Chinese).
29.
ZhangL.B., LiH.X., ZhouX.Z., et al., Multi-granularity cost-sensitive three-way decision for face recognition, Journal of Shandon University: Natural Science49(8) (2014), 48–57. (In Chinese).
30.
ZhaoY.P., An algorithm for attribute reduction of incomplete information system, In: Intelligent Computing and Intelligent Systems 2010 IEEE International Conference on IEEE, 2, 2010, pp. 635–638.
31.
YaoY.Y., Three-way decisions and cognitive computing, Cognitive Computation8(4) (2016), 543–554.
32.
XuZ.S. and HuiH., Models for intuitionistic fuzzy multiple attribute decision making, International Journal of Information Technology & Decision Making9(02) (2010), 267–280.
33.
LiuD., LiangD.C. and WangC.C., A novel three-way decision model based on incomplete information system, Know-ledge-Based Systems91 (2016), 32–45.
34.
ShiZ.H., ZhangD.H. and LiuK., A TOPSIS method based on incomplete intuitionistic fuzzy information, Mathematics Practice and Theory42(19) (2012), 234–240. (In Chinese).
35.
YangX.P. and AnH.T., Three-way decisions based on intuitionistic fuzzy sets, In: International Joint Conference on Rough Sets, Springer, Cham, 2017, pp. 290–299.
36.
SzmidtE. and KacprzykJ., Distances between intuitionistic fuzzy sets, Fuzzy Sets and Systems114(3) (2000), 505–518.
37.
KullbackS. and LeiblerR.A., On Information and sufficiency, Annals of Mathematical Statistics22(22) (1951), 79–86.
38.
LiuD., LiT.R., MiaoD.Q., et al., Three-way decision and granular computing. Beijing: Science Press, 2013, pp. 14–41. (In Chinese).
39.
XueZ.A., XinX.W., YuanY.L., et al., Research on the Three-way Decisions model based on intuitionistic fuzzy possibility measures, Journal of Nanjing University: Natural Sciences52(6) (2016), 1065–1074. (In Chinese).
40.
WangY.M., Using the method of maximizing deviation to make decision for multiindices, Systems Engineering and Electronics8(3) (1997), 21–26.
