In this paper, a single-granulation dual hesitant fuzzy rough set model based on dual hesitant fuzzy tolerance relations is first introduced. By the combination of multi-granulation rough sets and the single-granulation dual hesitant fuzzy rough sets, we then develop a new multi-granulation rough set model, called a multi-granulation dual hesitant fuzzy rough set. In the multi-granulation framework, two types of multi-granulation dual hesitant fuzzy rough sets are proposed, which are named the optimistic multi-granulation dual hesitant fuzzy rough sets and pessimistic multi-granulation dual hesitant fuzzy rough sets. Finally, the relationships among the single-granulation dual hesitant fuzzy rough sets, optimistic multi-granulation dual hesitant fuzzy rough sets and pessimistic multi-granulation dual hesitant fuzzy rough sets are investigated.
AtanassovK., Intuitionistic fuzzy sets, Fuzzy Sets and Systems20 (1986), 87–96.
2.
ChenN., XuZ.S. and XiaM.M., Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis, Applied Mathematical Modelling37 (2013), 2197–2211.
3.
ChenY.F., PengX.D., GuanG.H. and JiangH.D., Approaches to multiple attribute decision making based on the correlation coefficient with dual hesitant fuzzy information, Journal of Intelligent and Fuzzy Systems26 (2014), 2547–2556.
4.
DuboisD. and PradeH., Rough fuzzy sets and fuzzy rough sets, International Journal of General Systems17 (1990), 191–209.
5.
FarhadiniaB., Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets, Information Sciences240 (2013), 129–144.
6.
FarhadiniaB., Correlation for dual hesitant fuzzy sets and dual interval-valued hesitant fuzzy Sets, International Journal of Intelligent Systems29 (2014), 184–205.
7.
HuangB., GuoC.X., ZhuangY.L., LiH.X. and ZhouX.Z., Intuitionistic fuzzy multigranulation rough sets, Information Sciences277 (2014), 299–320.
8.
JenaS.P. and GhoshS.K., Intuitionistic fuzzy rough sets, Notes on Intuitionistic Fuzzy Sets8 (2002), 1–18.
9.
LiuC.H. and WangM.Z., Covering fuzzy rough set based on multigranulations, in: International Conference on Uncertainty Reasoning and Knowledge Engineering2011, pp. 146–149.
10.
LiuC.H. and MiaoD.Q., Covering Rough Set Model Based on Multigranulations, RSFDGRc, 2011, pp. 87–90.
11.
LinG.P., QianY.H. and LiJ.J., NMGRS: Neighborhood-based multigranulation rough sets, International Journal of Approximate Reasoning53(7) (2012), 1080–1093.
12.
LinG.P., LiangJ.Y. and QianY.H., Multigranulation rough sets: From partition to covering, Information Sciences241 (2013), 101–118.
13.
LiaoH.C. and XuZ.S., A VIKOR-based method for hesitant fuzzy multi-criteria decision making, Fuzzy Optimization Decision Making12(4) (2013), 373–392.
14.
LiaoH.C. and XuZ.S., Subtraction and division operations over hesitant fuzzy sets, Journal of Intelligent and Fuzzy Systems27 (2014), 65–72.
15.
LiaoH.C. and XuZ.S., Some new hybrid weighted aggregation operators under hesitant fuzzy multi-criteria decision making environment, Journal of Intelligent and Fuzzy Systems26(4) (2014), 1601–1617.
16.
LiaoH.C. and XuZ.S., Extended hesitant fuzzy hybrid weighted aggregation operators and their application in decision making, Soft Computing (2015). 10.1007/s00500-014-1422-6.
17.
LiaoH.C., XuZ.S. and ZengX.J., Novel correlation coefficients between hesitant fuzzy sets and their application in decision making, Knowledge-Based Systems82 (2015), 115–127.
18.
LiaoH.C., XuZ.S. and XiaM.M., Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making, International Journal of Information Technology and Decision Making13(1) (2014), 47–76.
19.
LiaoH.C. and XuZ.S., Satisfaction degree based interactive decision making method under hesitant fuzzy environment with incomplete weights, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems22(4) (2014), 553–572.
20.
LiaoH.C., XuZ.S. and XuJ.P., An approach to hesitant fuzzy multi-stage multi-criterion decision making, Kybernetes43(9/10) (2014), 1447–1468.
21.
LiuH.F., XuZ.S. and LiaoH.C., The multiplicative consistency index of hesitant fuzzy preference relation, IEEE Transactions on Fuzzy Systems (2012). 10.1109/TFUZZ.2015.2426315.
22.
LiangJ.Y., WangF., DangC.Y. and QianY.H., An efficient rough feature selection algorithm with a multi-granulation view, International Journal of Approximate Reasoning53 (2015), 912–926.
23.
MiyamotoS., Multisets and fuzzy multisets, in: LiuZ.Q., MiyamotoS., (Eds.), Soft Computing and Human-Centered
Machines, Springer, Berlin, Germany, 2000, pp. 9–33.
24.
NandaS. and MajumdaS., Fuzzy rough sets, Fuzzy Sets and Systems45 (1992), 157–160
25.
PawlakZ., Rough sets, International Journal of Computer Information Sciences11 (1982), 145–172.
26.
PawlakZ., Rough Sets-Theoretical Aspects to Reasoning about Data, Kluwer Academic Publisher, Boston, 1991.
27.
PedryczW., Granular Computing: Analysis and Design of Intelligent Systems, CRC Press/Francis Taylor, Boca Raton, 2013.
28.
QianY.H., LiangJ.Y., YaoY.Y. and DangC.Y., MGRS: A multigranulation rough set, Information Scinences180 (2010), 949–970.
29.
QianY.H., LiangJ.Y., PedryczW. and DangC.Y., An efficient accelerator for attribute reduction from incomplete data in rough set framework, Pattern Recognition44 (2011), 1658–1670.
30.
QianY.H., LiangJ.Y. and DangC.Y., Incomplete multigranulation rough set, IEEE Transactions on Systems, Man and Cybernetics ĺC Part A20 (2010), 420–431.
31.
QianH., ZhangH., SangY.L. and LiangJ.Y., Multigranulation decision-theoretic rough sets, International Journal of Approximate Reasoning55 (2014), 225–237.
32.
RadzikowskaA.M. and KerreE.E., A comparative study of fuzzy rough sets, Fuzzy Sets and Systems126 (2002), 137–155.
33.
RodrĺłguezR.M., MartĺłnezL. and HerreraF., Hesitant fuzzy linguistic term sets for decision making, IEEE Transactions on Fuzzy Systems1 (2012), 109–119.
34.
SheY.H. and HeX.L., On the structure of the multigranulation rough set model, Knowledge-Based Systems36 (2012), 81–92.
35.
TiwariS.P. and SrivastavaArun K., Fuzzy rough sets, fuzzy preorders and fuzzy topologies, Fuzzy Sets and Systems210 (2013), 63–68.
36.
TorraV. and NarukawaY., On hesitant fuzzy sets and decision, Jeju Island, Korea, The 18th IEEE International Conference on Fuzzy Systems2009, pp. 1378–1382.
37.
TorraV., Hesitant fuzzy sets, International Journal of Intelligent Systems25 (2010), 529–539.
38.
WangH.J., ZhaoX.F. and WeiG.W., Dual hesitant fuzzy aggregation operators in multiple attribute decision making, Journal of Intelligent and Fuzzy Systems26 (2014), 2281–2290.
39.
WuW.Z., MiJ.S. and ZhangW.X., Generalized fuzzy rough sets, Information Sciences151 (2003), 263–282.
40.
WuW.Z. and ZhangW.X., Constructive and axiomatic approaches of fuzzy approximation operators, Information Sciences159 (2004), 233–254.
41.
XiaM.M. and XuZ.S., Hesitant fuzzy information aggregation in decision making, International Journal of Approximate Reasoning52 (2011), 395–407.
42.
XuW.H., WangQ.R. and ZhangX.T., Multi-granulation fuzzy rough sets in a fuzzy tolerance approximation space, International Journal of Fuzzy Systems13(4) (2011), 246–259.
43.
XuW.H., WangQ.R. and LuoS.Q., Multi-granulation fuzzy rough sets, Journal of Intelligent and Fuzzy Systems26 (2014), 1323–1340.
44.
XuW.H., SunW.X., ZhangX.Y. and ZhangW.X., Multiple granulation rough set approach to ordered information systems, International Journal of General Systems41(5) (2012), 475–501.
45.
XuZ.S. and XiaM.M., Distance and similarity measures for hesitant fuzzy sets, Information Sciences181 (2011), 2128–2138.
46.
XuZ.S. and XiaM.M., On distance and correlation measures of hesitant fuzzy information, International Journal of Intelligent Systems26 (2011), 410–425.
47.
XuZ.S. and ZhangX., Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information, Knowledge-Based Systems52 (2013), 53–64.
48.
YeungD.S., ChenD.G., TsangE.C.C., LeeJ.W.T. and WangX.Z., On the generalization of fuzzy rough sets, IEEE Transactions on Fuzzy Systems13 (2005), 343–361.
49.
YeJ., Correlation coefficient of dual hesitant fuzzy sets and its application to multiple attribute decision making, Applied Mathematical Modelling38 (2014), 659–666.
50.
YangX.B., SongX.N., QiY.S. and YangJ.Y., Constructive and axiomatic approaches to hesitant fuzzy rough set, Soft Computing18 (2014), 1067–1077.
51.
YangX.B., SongX.N. and DouH.L., Multi-granulation rough set: from crisp to fuzzy case, Annals of Fuzzy Mathematics and Informatics1(1) (2011), 55–70.
52.
YangX.B., QianY.H. and YangJ.Y., Hierarchical structures on multigranulation spaces, Journal Of Computer Science and Technology27 (2012), 1169–1183.
53.
ZhuB., XuZ.S. and XiaM.M., Dual hesitant fuzzy sets, Journal of Applied Mathematics2012 (2012), 13. Article ID 879629.
54.
ZhangH.D., ShuL. and LiaoS.L., Intuitionistic fuzzy soft rough set and its application in decision making, Abstract and Applied Analysis2014 (2014), 13Article ID 287314.
55.
ZhangH.D., ShuL. and LiaoS.L., On interval-valued hesitant fuzzy rough approximation operators, Soft Computing (2014). DOI: 10.1007/s00500-014-1490-7
56.
ZhangH.D. and ShuL., Generalized interval-valued fuzzy rough set and its application in decision making, International Journal of Fuzzy Systems17(2) (2015), 279–291.
57.
ZhangH.Y., LeungY. and ZhouL., Variable-precision-dominance-based rough set approach to interval-valued information systems, Information Sciences244 (2013), 75–91.
58.
ZhouL. and WuW.Z., On genernalized intuitionistic fuzzy approximation operators, Information Sciences178 (2008), 2448–2465.
59.
ZhouL. and WuW.Z., On characterization of intuitonistic fuzzy rough sets based on intuitionistic fuzzy implicators, Information Sciences179 (2009), 883–898.
60.
ZadehL.A., Fuzzy sets, Information and Control8 (1965), 378–352.
61.
ZhangN. and WeiG., Extension of VIKOR method for decision making problem based on hesitant fuzzy set, Applied Mathematical Modelling37(7) (2013), 4938–4947.
62.
ZhangX.H., ZhouB. and LiP., A general frame for intuitionistic fuzzy rough sets, Information Sciences216 (2012), 34–49.
63.
ZhangZ.M., Generalized intuitionistic fuzzy rough sets based on intuitionistic fuzzy coverings, Information Sciences198 (2012), 186–206.
