In this paper, we establish a systematic framework for the study of hesitant fuzzy compatible rough sets by a constructive approach. In the constructive approach, we introduce the concept of lower and upper hesitant fuzzy compatible rough approximation operators and also investigate some properties of this model. Then the concepts of roughness measure and approximate precision of a crisp set in hesitant fuzzy compatible approximation space are proposed and their basic properties are further discussed. Based on the hesitant fuzzy compatible rough sets, a novel decision-making approach to hesitant fuzzy soft sets is established. Meanwhile, a practical example is provided to demonstrate the effectiveness of this method. Finally, by comparing the novel method with the decision making method based on fuzzy soft sets, we point out some advantages of the novel method.
BabithaK.V. and JohnS.J.
, Hesitant fuzzy soft sets, Journal of New Results in Science3 (2013), 98–107.
5.
CornelisC., CockM.D. and KerreE.E.
, Intuitionistic fuzzy rough sets: At the crossroads of imperfect knowledge, Expert Systems with Application20 (2003), 260–270.
6.
ChakrabartyK., GedeonT. and KoczyL.
, Intuitionistic fuzzy rough set, in: Proceedings of Fourth Joint Conference on Information Sciences (JCIS), Durham, NC, 1998, pp. 211–214.
7.
CagmanN. and EnginogluS.
, Soft matrix theory and its decision making, Computers and Mathematics with Applications59 (2010), 3308–3314.
8.
CagmanN. and EnginogluS.
, Fuzzy soft matrix theory and its application in decision making, Iranian Journal of Fuzzy Systems9(1) (2012), 109–119.
9.
ChenN., XuZ.S. and XiaM.M.
, Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis, Applied Mathematical Modelling37 (2013), 2197–2211.
10.
DuboisD. and PradeH.
, Rough fuzzy sets and fuzzy rough sets, International Journal of General Systems17 (1990), 191–209.
11.
FarhadiniaB.
, Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets, Information Sciences240 (2013), 129–144.
12.
FengF., JunY.B., LiuX.Y. and LiL.F.
, An adjustable approach to fuzzy soft set based decision making, Journal of Computational and Applied Mathematics234 (2010), 10–20.
13.
GorzalczanyM.B.
, A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets and Systems21 (1987), 1–17.
14.
JenaS.P. and GhoshS.K.
, Intuitionistic fuzzy rough sets, Notes on Intuitionistic Fuzzy Sets8 (2002), 1–18.
15.
LiuG.L.
, Rough set theory based on two universal sets and its applications, Knowledge-Based Systems23(2) (2010), 110–115.
16.
LiaoH.C. and XuZ.S.
, A VIKOR-based method for hesitant fuzzy multi-criteria decision making, Fuzzy Optimization Decision Making12 (2013), 373–392.
17.
LiaoH.C. and XuZ.S., Hesitant Fuzzy Decision Making Methodologies and Applications, Springer International Publishing, Switzerland, 2017.
18.
LiT.J. and ZhangW.X.
, Rough fuzzy approximations on two universes of discourse, Information Sciences178 (2008), 892–906.
19.
MolodtsovD.
, Soft set theory-First results, Computers and Mathematics with Applications37 (1999), 19–31.
20.
MajiP.K., BiswasR. and RoyA.R.
, Fuzzy soft set, Journal of Fuzzy Mathematics9(3) (2001), 589–602.
21.
MaX.L., LiuQ. and ZhanJ.M.
, A survey of decision making methods based on certain hybrid soft set models, Artificial Intelligence Review47 (2017), 507–530.
22.
NandaS. and MajumdaS.
, Fuzzy rough sets, Fuzzy Sets and Systems45 (1992), 157–160.
23.
PawlakZ.
, Rough sets, International Journal of Computer Information Sciences11 (1982), 145–172.
24.
PawlakZ., Rough Sets-Theoretical Aspects to Reasoning about Data, Kluwer Academic Publisher, Boston, 1991.
25.
RadzikowskaA.M. and KerreE.E.
, A comparative study of fuzzy rough sets, Fuzzy Sets and Systems126 (2002), 137–155.
26.
RodrĺłguezR.M., MartL.ĺłnez and HerreraF.
, Hesitant fuzzy linguistic term sets for decision making, IEEE Transactions on Fuzzy Systems1 (2012), 109–119.
27.
SunB.Z., GongZ.T. and ChenD.G.
, Fuzzy rough set theory for the interval-valued fuzzy information systems, Information Sciences178 (2008), 2794–2815.
28.
SunB.Z. and MaW.M.
, Fuzzy rough set model on two different universes and its application, Applied Mathematical Modelling35 (2011), 1798–1809.
29.
SunB.Z., MaW.M. and LiuQ.
, An approach to decision making based on intuitionistic fuzzy rough sets over two universes, Journal of the Operational Research Society64 (2013), 1079–1089.
30.
SamantaS.K. and MondalT.K.
, Intuitionistic fuzzy rough sets and rough intuitionistic fuzzy sets, Journal of Fuzzy Mathematics9 (2001), 561–582.
31.
ShenY.H. and WandF.X.
, Variable precision rough set model over two universes and its properties, Soft Computing15(3) (2011), 557–567.
32.
ThieleH.
, On aximatic characterisation of fuzzy approximation operators: I The I. rough fuzzy set based case, in: Proceeding of the 31st IEEE International Symposium on Multiple-Valued Logic, 2001, pp. 330–335.
33.
TiwariS.P. and SrivastavaA.K., Fuzzy rough sets, fuzzy preorders and fuzzy topologies, Fuzzy Sets and Systems210 (2013), 63–68.
34.
TorraV.
, Hesitant fuzzy sets, International Journal of Intelligent Systems25 (2010), 529–539.
35.
WangF.Q., LiX.H. and ChenX.H.
, Hesitant fuzzy soft set and its applications in multicriteria decision making, Journal of Applied Mathematics2014, 10. ArticleID 643785.
36.
WuW.Z., LeungY. and MiJ.S., On characterizations of (I, T)-fuzzy rough approximation operators, Fuzzy Sets and Systems154 (2005), 76–102.
37.
WuW.Z., MiJ.S. and ZhangW.X.
, Generalized fuzzy rough sets, Information Sciences151 (2003), 263–282.
38.
WuW.Z. and ZhangW.X.
, Constructive and axiomatic approaches of fuzzy approximation operators, Information Sciences159 (2004), 233–254.
39.
WuW.Z., LeungY. and ZhangW.X., On generalized rough fuzzy approximation operators, Transactions on Rough sets V, Lecture Notes in Computer Science4100 (2006), 263–284.
40.
XiaM.M. and XuZ.S.
, Hesitant fuzzy information aggregation in decision making, International Journal of Approximate Reasoning52 (2011), 395–407.
41.
XuZ.S., Hesitant Fuzzy Sets Theory, Springer International Publishing, Switzerland, 2014.
42.
XuZ.S. and XiaM.M.
, Distance and similarity measures for hesitant fuzzy sets, Information Sciences181 (2011), 2128–2138.
43.
XuZ.S. and XiaM.M.
, On distance and correlation measures of hesitant fuzzy information, International Journal of Intelligent Systems26 (2011), 410–425.
44.
XuZ.S. and ZhangX.
, Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information, Knowledge-Based Systems52(0) (2013), 53–64.
45.
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.
46.
YangH.L., LiS.G., WangS.Y. and WangJ.
, Bipolar fuzzy rough set model on two different universes and its application, Knowledge-Based Systems35 (2012), 94–101.
47.
YangH.L., LiS.G., GuoZ.L. and MaC.H.
, Transformation of bipolar fuzzy rough set models, Knowledge-Based Systems27 (2012), 60–68.
48.
YangX.B., SongX.N., QiY.S. and YangJ.Y.
, Constructive and axiomatic approaches to hesitant fuzzy rough set, Soft Computing18 (2014), 1067–1077.
49.
YaoY.Y.
, Generalized rough set model, in: PolkowskiL. and SkowronA. (Eds.), Rough Sets in Knowledge Discovery. 1. Methodology and Applications Physica-Verlag, Berlin, 1998, pp. 286–318.
50.
ZhanJ.M., LiuQ. and HerawanT.
, A novel soft rough set: Soft rough hemirings and its multicriteria group decision making, Applied Soft Computing54 (2017), 393–402.
51.
ZhanJ.M., AliM.I. and MehmoodN.
, On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods, Applied Soft Computing56 (2017), 446–457.
52.
ZhanJ.M. and ZhuK.Y.
, A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making, Soft Computing21 (2017), 1923–1936.
53.
ZhanJ.M., LiuQ. and ZhuW.
, Another approach to rough soft hemirings and corresponding decision making, Soft Computing21 (2017), 3769–3780.
54.
ZhangH.D., ShuL. and LiaoS.L.
, Intuitionistic fuzzy soft rough set and its application in decision making, Abstract and Applied Analysis2014 (2014), 13. Article ID 287314.
55.
ZhangH.D., ShuL. and LiaoS.L.
, On interval-valued hesitant fuzzy rough approximation operators, Soft Computing20 (2016), 189–209.
56.
ZhangH.D., ShuL. and LiaoS.L.
, Hesitant fuzzy rough set over two universes and its application in decision making, Soft Computing21 (2017), 1803–1816.
57.
ZhangH.D., ShuL., LiaoS.L. and XiawuC.R.
, Dual hesitant fuzzy rough set and its application, Soft Computing21 (2017), 3287–3305.
58.
ZhangH.Y., ZhangW.X. and WuW.Z.
, On characterization of generalized interval-valued fuzzy rough sets on two universes of discourse, International Journal of Approximate Reasoning51 (2009), 56–70.
59.
ZhouL. and WuW.Z.
, On genernalized intuitionistic fuzzy approximation operators, Information Sciences178 (2008), 2448–2465.
60.
ZhouL. and WuW.Z.
, On characterization of intuitonistic fuzzy rough sets based on intuitionistic fuzzy implicators, Information Sciences179 (2009), 883–898.
61.
ZadehL.A.
, Fuzzy sets, Information and Control8 (1965), 378–352.
62.
ZhangN. and WeiG.
, Extension of VIKOR method for decision making problem based on hesitant fuzzy set, Applied Mathematical Modelling37(7) (2013), 4938–4947.
63.
ZhangX.H., ZhouB. and LiP.
, A general frame for intuitionistic fuzzy rough sets, Information Sciences216 (2012), 34–49.
64.
ZhangZ.M.
, On characterization of generalized interval type-2 fuzzy rough sets, Information Sciences219 (2013), 124–150.
65.
ZhangZ.M.
, A rough set approach to intuitionistic fuzzy soft set based decision making, Applied Mathematical Modelling36 (2012), 4605–4633.
