In this paper, we first define interval-valued intuitionistic fuzzy parameterized soft sets by combining the interval-valued intuitionistic fuzzy sets and the soft sets from parametrization point of view. By using soft level sets we then construct a parameter reduction method to obtain a better decision making. We finally give a numerical example to show the method working successfully for problems containing uncertain data.
AliM.I., FengF., LiuX., MinW.K. and ShabirM., On some new operations in soft set theory, Computers and Mathematics with Applications57 (2009), 1547–1553.
2.
AtanassovK., Intuitionistic fuzzy sets, Fuzzy Sets and Systems20 (1986), 87–96.
3.
AtanassovK. and GarovG., Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems31 (1989), 343–349.
4.
ÇağmanN. and
EnginoğluS., Soft set theory and uni-int decision making, European Journal of Operational Research207 (2010), 848–855.
5.
ÇağmanN., ÇitakF. and EnginoğluS., FP-soft set theory and its applications, Annals of Fuzzy Mathematics and Informatics2/2 (2011), 219–226.
6.
ÇağmanN. and
KarataşS., Intuitionistic fuzzy soft set theory and its decision making, Journal of Intelligent and Fuzzy Systems24/4 (2013), 829–836.
7.
ÇağmanN.,
ErdoğanF. and
EnginoğluS., FP-soft set theory and its applications, Annals of Fuzzy Mathematics and informatics2/2 (2011), 219–226.
8.
ÇağmanN. and
DeliI., Means of FP-soft sets and its applications, Hacettepe Journal of Mathematics and Statistics41(5) (2012), 615–625.
9.
ÇağmanN. and
DeliI., Product of FP-soft sets and its applications, Hacettepe Journal of Mathematics and Statistics41(3) (2012), 365–374.
10.
ÇağmanN., Contributions to the theory of soft sets, Journal of New Results in Science (4) (2014), 33–41.
11.
DeliI. and ÇağmanN., Intuitionistic fuzzy parameterized soft set theory and its decision making, Applied Soft Computing28 (2015), 109–113.
12.
DeliI. and ÇağmanN., Relations on FP-soft sets applied to decision making problems, Journal of New Theory3 (2015), 98–107.
13.
DindaB. and SamantaT.K., Relations on intuitionistic fuzzy soft sets, Gen Math Notes1/2 (2010), 74–83.
14.
FengF., JunY.B. and ZhaoX., Soft semirings, Computers and Mathematics with Applications56/10 (2008), 2621–2628.
15.
FengF., JunY.B., LiuX. and LiL., An adjustable approach to fuzzy soft sets based decision making, Journal of Computational and Applied Mathematics234 (2010), 10–20.
16.
FengF., LiuX., FoteaV.L. and JunY.B., Soft sets and soft rough sets, Information Sciences181 (2011), 1125–1137.
17.
FengF., LiC., DavvazB. and Irfan AliM., Soft sets combined with fuzzy sets and rough sets: A tentative approach, Soft Computing14 (2010), 899–911.
18.
GorzalczanyM.B., A method of inference in approximate reasoning based on interval valued fuzzy sets, Fuzzy Sets and Systems21 (1987), 1–17.
19.
JiangY., TangY., ChenQ., LiuH. and TangJ., Interval-valued intuitionistic fuzzy soft sets and their properties, Computers and Mathematics with Applications60 (2010), 906–918.
20.
JiangY., TangY. and ChenQ., An adjustable approach to intuitionistic fuzzy soft sets based decision making, Applied Mathematical Modelling35 (2011), 824–836.
21.
MajiP.K. and RoyA.R., An application of soft sets in a decision making problem, Computers and Mathematics with Applications44 (2002), 1077–1083.
22.
MajiP.K., BiswasR. and RoyA.R., Fuzzy soft sets, Journal of Fuzzy Mathematics9(3) (2001), 589–602.
23.
MolodtsovD.A., Soft set theory-first results, Computers and Mathematics with Applications37 (1999), 19–31.
24.
MukherjeeA. and ChakrabortyS.B., On Intuitionistic fuzzy soft relations, Bulletin of Kerala Mathematics Association5/1 (2008), 35–42.
25.
PawlakZ., Rough sets, International Journal of Information and Computer Sciences11 (1982), 341–356.
26.
PengJ.J., WangJ.Q., WuX.H., ZhangH.Y. and ChenX.H., The Fuzzy Cross-entropy for Intuitionistic Hesitant Fuzzy Sets and its Application in Multi-criteria Decision making, International Journal of Systems Science (2015). DOI: 10.1080/00207721.2014.993744
27.
SezginA. and AtagünA.O., On operations of soft sets, Computers and Mathematics with Applications61/5 (2011), 1457–1467.
28.
SomT., On the theory of soft sets, soft relation and fuzzy soft relation, Proc of the National Conference on Uncertainty: A Mathematical Approach, UAMA-06, Burdwan, 2006, pp. 1–9.
29.
SutD.K., An application of fuzzy soft relation in decision making problems, International Journal of Mathematics Trends and Technology3/2 (2012), 51–54.
30.
XiaoZ., GongK. and ZouY., A combined forecasting approach based on fuzzy soft sets, J Comput Appl Math228 (2009), 326–333.
31.
WangJ.Q. and ZhangH.Y., Multi-criteria decision-making approach based on Atanassov’s intuitionistic fuzzy sets with incomplete certain information on weights, IEEE Transactions on Fuzzy Systems21(3) (2013), 510–515.
32.
WangJ.Q., NieR.R., ZhangH.Y. and ChenX.H., New operators on triangular intuitionistic fuzzy numbers and their applications in system fault analysis, Information Sciences251 (2013), 79–95.
33.
WangJ.Q., NieR.R., ZhangH.Y. and ChenX.H., Intuitionistic fuzzy multi-criteria decision-making method based on evidential reasoning, Applied Soft Computing13(4) (2013), 1823–1831.
34.
WangJ.Q., LiK.J., ZhangH.Y. and ChenX.H., A score function based on relative entropy and its application in intuitionistic normal fuzzy multiple criteria decision making, Journal of Intelligent and Fuzzy Systems25(3) (2013), 567–576.
35.
WangJ.Q., ZhouP., LiK.J., ZhangH.Y. and ChenX.H., Multicriteria decision-making method based on normal intuitionistic fuzzy-induced generalized aggregation operator, TOP22 (2014), 1103–1122.
36.
WangX.F., WangJ.Q. and YangW.E., Multi-criteria group decision making method based on intuitionistic linguistic aggregation operators, Journal of Intelligent and Fuzzy Systems26(1) (2014), 115–125.
37.
YangX., LinT.Y., YangJ., LiY. and YuD., Combination of interval-valued fuzzy set and soft set, Comput Math Appl58 (2009), 521–527.
38.
ZadehL.A., Fuzzy Sets, Inform and Control8 (1965), 338–353.
39.
ZhangZ., WangC., TianD. and LiK., A novel approach to interval-valued intuitionistic fuzzy soft set based decision making, Applied Mathematical Modellingxxx (2013) xxx (in press).
40.
ZouY. and XiaoZ., Data analysis approaches of soft sets under incomplete information, Knowl Base Syst21 (2008), 941–945.