Three-way decisions model proposed by Yao gives a semantic interpretation of positive region, negative region and boundary region. This model was developed in the framework of classical rough set, the approached target concept is a crisp set, the employed knowledge is a equivalence relation. In this paper, we extend the three-way decisions model to rough fuzzy set. Specifically, the target concept is extended to a fuzzy set, while the used knowledge is also a equivalence relation. An example is given to illustrate the computation processes of the proposed three-way decisions model. The extended model can deal with the problems described by fuzzy decision tables with symbolic-valued conditional attributes and fuzzy decision attributes.
PawlakZ., Rough sets, International Journal of Information and Computer Sciences11 (1982), 341–356.
2.
ZiarkoW., Variable precision rough set model, Journal of Computer and System Sciences46(93) (1993), 39–59.
3.
DuboisD. and PradeH., Rough fuzzy sets and fuzzy rough sets, International Journal of General Systems17(2) (1990), 191–208.
4.
YaoY.Y. and WongS.K.M., A decision theoretic framework for approximating concepts, International Journal of Manmachine Studies37(6) (1992), 793–809.
5.
YangY.Y., ChenD.G., WangH., et al., Fuzzy rough set based incremental attribute reduction from dynamic data with sample arriving, Fuzzy Sets and Systems312 (2017), 66–86.
6.
YangY.Y., ChenD.G. and WangH., Active sample selection based incremental algorithm for attribute reduction with rough sets, IEEE Transactions on Fuzzy Systems25(4) (2017), 825–838.
7.
WangC.Z., ShaoM.W., HeQ., et al., Feature subset selection based on fuzzy neighborhood roughsets, Knowledge-Based Systems111 (2016), 173–179.
8.
WangC.Z., QiY.H., ShaoM.W., et al., A fitting model for feature selection with fuzzy rough sets, IEEE Transaction on Fuzzy Systems25(4) (2017), 741–753.
9.
ZhangX., MeiC.L., ChenD.G., et al., Feature selection in mixed data: A method using a novel fuzzy rough set-based information entropy, Pattern Recognition56 (2016), 1–15.
10.
HuQ.Q., ZhangL.J., ZhouY., et al., Large-scale multimodality attribute reduction with multi-kernel fuzzy rough sets, IEEE Transactions on Fuzzy Systems (2017). doi: 10.1109/TFUZZ.2017.2647966
11.
DaiJ.H., HuQ.H., HuH., et al., Neighbor inconsistent pair selection for attribute reduction by rough set approach, IEEE Transactions on Fuzzy Systems (2017). doi: 10.1109/TFUZZ.2017.2698420.
12.
WangX.Z., ZhaiJ.H. and LuS.X., Induction of multiple fuzzy decision trees based on rough set technique, Information Sciences178(16) (2008), 3188–3202.
13.
ZhaoS.Y., TsangE.C.C., ChenD.G., et al., Building a rulebased classifierłA fuzzy-rough set approach, IEEE Transactions on Knowledge and Data Engineering22(5) (2009), 624–638.
14.
ZhaoS.Y., ChenH., LiC.P., et al., A novel approach to building a robust fuzzy rough classifier, IEEE Transactions on Fuzzy Systems23(4) (2015), 769–786.
15.
NaumanM., AzamN. and YaoJ.T., A three-way decision making approach to malware analysis using probabilistic rough sets, Information Sciences374 (2016), 193–209.
16.
XiongW., SuQ.Y. and LiJ.L., The group decision-making rules based on rough sets on large scale engineering emergency, Systems Engineering Procedia4 (2012), 331–337.
17.
HeY.D., ChenH.Y., HeZ., et al., Multi-attribute decision making based on neutral averaging operators for intuitionistic fuzzy information, Applied Soft Computing27 (2015), 64–76.
18.
HeY.D., HeZ., ShiL.X., et al., Multiple attribute group decision making based on IVHFPBMs and a new ranking method for interval-valued hesitant fuzzy information, Computers & Industrial Engineering99 (2016), 63–77.
19.
LiuD., LiangD.C. and WangC.C., A novel three-way decision model based on incomplete information system, Knowledge Based Systems91 (2016), 32–45.
20.
LiangD.C., LiuD. and KobinaA., Three-way group decisions with decision-theoretic rough sets, Information Sciences345 (2016), 46–64.
21.
ZhaoX.R. and HuB.Q., Fuzzy probabilistic rough sets and their corresponding three-way decisions, Knowledge-Based Systems91 (2016), 126–142.
22.
YaoY.Y., Interval sets and three-way concept analysis in incomplete contexts, International Journal of Machine Learning and Cybernetics8(1) (2017), 3–20.
23.
PetersJ.F. and RamannaS., Proximal three-way decisions: Theory and applications in social networks, Knowledge-Based Systems91 (2016), 4–15.
24.
ShivhareR. and CherukuriA.K., Three-way conceptual approach for cognitive memory functionalities, International Journal of Machine Learning and Cybernetics8(1) (2017), 21–34.
25.
SinghP.K., Three-way fuzzy concept lattice representation using neutrosophic set, International Journal of Machine Learning and Cybernetics8(1) (2017), 69–79.
26.
YaoJ.T. and AzamN., Web-based medical decision support systems for three-way medical decision making with gametheoretic rough sets, IEEE Transactions on Fuzzy Systems23(1) (2015), 3–15.
27.
ZhangH.R. and MinF., Three-way recommender systems based on random forests, Knowledge-Based Systems91 (2016), 275–286.
28.
LiJ., HuangC.C., QiJ.J., et al., Three-way cognitive concept learning via multi-granularity, Information Sciences378(1) (2017), 244–263.
29.
YuH., ZhangC. and WangG.Y., A tree-based incremental overlapping clustering method using the three-way decision theory, Knowledge-Based Systems91 (2016), 189–203.
30.
ZhangH.R., MinF. and ShiB., Regression-based three-way recommendation, Information Sciences378 (2017), 444–461.
31.
LiH.X., ZhangL.B., HuangB., et al., Sequential three-way decision and granulation for cost-sensitive face recognition, Knowledge-Based Systems91 (2016), 241–251.
32.
LiW.W., HuangZ.Q. and LiQ., Three-way decisions based software defect prediction, Knowledge-Based Systems91 (2016), 263–274.
33.
QiJ.J., QianT. and WeiL., The connections between threeway and classical concept lattices, Knowledge-Based Systems91 (2016), 143–151.
34.
ChenJ., ZhangY.P. and ZhaoS., Multi-granular mining for boundary regions in three-way decision theory, Knowledge-Based Systems91 (2016), 287–292.
35.
FujitaH., LiT.R. and YaoY.Y., Advances in three-way decisions and granular computing, Knowledge-Based Systems91 (2016), 1–3.
RaoD.V. and SarmaV.V.S., A rough-fuzzy approach for retrieval of candidate components for software reuse, Pattern Recognition Letters24(6) (2003), 875–886.
38.
MajiP. and PalS.K., Rough-fuzzy C-medoids algorithm and selection of bio-basis for amino acid sequence analysis,IEEE Transactions on Knowledge and Data Engineering19(6) (2007), 859–872.
39.
JensenR. and ShenQ., Fuzzy-rough attribute reduction with application to web categorization, Fuzzy Sets and Systems141(3) (2004), 469–485.
40.
JensenR. and ParthaláinN.M., Towards scalable fuzzyCrough feature selection, Information Sciences323 (2015), 1–15.
41.
KrupkaJ. and JiravaP., Rough-fuzzy classifier modeling using data repository sets, Procedia Computer Science35 (2014), 701–709.
ShiJ., LeiY., ZhouY., et al., Enhanced rough-fuzzy c-means algorithm with strict rough sets properties, Applied Soft Computing46 (2016), 827–850.
44.
SaltosR., A rough-fuzzy approach for support vector clustering, Information Sciences339 (2016), 353–368.
45.
HanY., ShiP. and ChenS., Bipolar-valued rough fuzzy set and its applications to the decision information system, IEEE Transactions on Fuzzy Systems23(6) (2015), 2358–2370.
46.
WenS.D. and BaoQ.H., Dominance-based rough fuzzy set approach and its application to rule induction, European Journal of Operational Research261(2) (2017), 690–703.
47.
YaoY.Y., Three-way decisions with probabilistic rough sets, Information Sciences180(3) (2010), 341–353.
48.
ZadehL.A., Fuzzy sets, Information and Control8(3) (1965), 338–353.
