The theory of soft sets is a powerful mathematical tool to handle the vagueness in data, while the m-polar fuzzy (mF, for short) sets have ability to deal with uncertainty as well as multi-polarity of the data in many situations. In this research article we present two novel hybrid models for soft computing, namely, m-polar fuzzy N-soft sets ((m, N)-soft sets, for short) and m-polar fuzzy N-soft rough sets ((m, N)-soft rough sets, for short). We define related concepts and investigate some of their fundamental properties. We also present applications of these hybrid models to multi-attribute decision-making.
AkramM., AdeelA. and AlcantudJ.C.R., Group decisionmaking methods based on hesitant N– soft sets, Expert Systems with Application115 (2019), 95–105.
2.
AkramM., AdeelA. and AlcantudJ.C.R., Fuzzy N-soft sets: A novel model with applications, Journal of Intelligent and Fuzzy Systems35(4) (2018), 4757–4771.
3.
AkramM., m-Polar fuzzy graphs-theory, methods & applications, Studies in Fuzziness and Soft Computing371 (2019), 1–284. Springer.
4.
AkramM. and AdeelA., Novel hybrid decision-making methods based on mF rough information, Granular Computing (2018). doi: 10.1007/s41066-018-00142-6.
5.
AkramM., AliG. and AlshehriN.O., A new multiattribute decision-making method based on m-polar fuzzy soft rough sets, Symmetry9(11) (2017). 271. https://doi.org/10.3390/sym9110271.
6.
AkramM., AliG., WaseemN. and DavvazB., Decisionmaking methods based on hybrid mF models, Journal of Intelligent and Fuzzy Systems35(3) (2018), 3387–3403.
7.
AlcantudJ.C.R. and LaruelleA., Dis & approval voting: A characterization, Social Choice and Welfare43(1) (2014), 1–10.
8.
AlcantudJ.C.R., A novel algorithm for fuzzy soft set based decision making from multiobserver input parameter data set, Information Fusion29 (2016), 142–148.
9.
AlcantudJ.C.R., Fuzzy soft set based decision making: A novel alternative approach, IFSA-EUSFLAT, 2015.
10.
AlcantudJ.C.R., Fuzzy soft set decision making algorithms: Some clarifications and reinterpretations, In Conference of the Spanish Association for Artificial Intelligence, 2016, pp. 479–488. Springer International Publishing.
11.
AlcantudJ.C.R., Cruz-RambaudS. and MuñozM.J., Torrecillas, Valuation fuzzy soft sets: A flexible fuzzy soft set based decision making procedure for the valuation of assets, Symmetry9 (2017), 253. doi: 10.3390/sym9110253.
12.
AlcantudJ.C.R. and MathewT.J., Separable fuzzy soft sets and decision making with positive and negative attributes, Applied Soft Computing59 (2017), 586–595.
13.
AliM.I., FengF., LiuX.Y., MinW.K. and ShabirM., On some new operations in soft set theory, Computers and Mathematics with Applications57(9) (2009), 1547–1553.
14.
AliM.I., A note on soft sets, rough soft sets and fuzzy soft sets, Applied Soft Computing11(4) (2011), 3329–3332.
15.
AliM.I., Another view on reduction of parameters in soft sets, Applied Soft Computing12(6) (2012), 1814–1821.
16.
AliM.I., MahmoodT., RehmanM.M.U. and AslamM.F., On lattice ordered soft sets, Applied Soft Computing36 (2015), 499–505.
17.
ChenJ., LiS., MaS. and WangX., m-polar fuzzy sets: An extension of bipolar fuzzy sets, The Scientific World Journal2014 (2014), 8. Article ID 416530.
18.
ChenS., LiuJ., WangH. and AugustoJ.C., Ordering based decision-making a survey, Information Fusion14(4) (2013), 521–531.
19.
DongY., LiuY., LiangH., ChiclanaF. and Herrera-ViedmaE., Strategic weight manipulation in multiple attribute decision making, Omega75 (2018), 154–164.
20.
DanjumaS., IsmailM.A. and HerawanT., An alternative approach to normal parameter reduction algorithm for soft set theory, IEEE Access5 (2017), 4732–4746.
21.
DanjumaS., HerawanT., IsmailM.A., ChiromaH., AbubakarA.I. and ZekiA.M., A review on soft set-based parameter reduction and decision making, IEEE Access5 (2017), 4671–4689.
22.
FatimahF., RosadiD., HakimR.B.F. and AlcantudJ.C.R., N-soft sets and their decision making algorithms, Soft Computing22(12) (2018), 3829–3842.
23.
FatimahF., RosadiD., HakimR.B.F. and AlcantudJ.C.R., Probabilistic soft sets and dual probabilistic soft sets in decision-making, Neural Computing and Applications (2017). https://doi.org/10.1007/s00521-017-3011-y.
24.
FengF., Soft rough sets applied to multicriteria group decision making, Annals of Fuzzy Mathematics and Informatics2(1) (2011), 69–80.
25.
FengF., LiC., DavvazB. and AliM.I., Soft sets combined with fuzzy sets and rough sets: A tentative approach, Soft Computing14(9) (2010), 899–911.
26.
FengF., LiuX., Leoreanu-FoteaV. and JunY.B., Soft sets and soft rough sets, Information Sciences181(6) (2011), 1125–1137.
27.
FengF., JunY.B., LiuX. and LiL., An adjustable approach to fuzzy soft set based decision-making, Journal of Computation and Applied Mathematics234(1) (2010), 10–20.
28.
HerawanT. and DerisM.M., On multi-soft sets construction in information systems, Springer, Berlin, Heidelberg, 2009, pp. 101–110.
29.
KongZ., GaoL. and WangL., Comment on: A fuzzy soft set theoretic approach to decision-making problem, Journal of Computational and Applied Mathematics223(2) (2009), 540–542.
30.
LiC.C., DongY. and HerreraF., A consensus model for largescale linguistic group decision making with a feedback recommendation based on clustered personalized individual semantics and opposing consensus groups, IEEE Transactions on Fuzzy Systems27(2) (2019), 221–233.
31.
LiuY., DongY., LiangH., ChiclanaF. and Herrera-ViedmaE., Multiple attribute strategic weight manipulation with minimum cost in a group decision making context with interval attribute weights information, IEEE Transactions on Systems, Man, and Cybernetics: Systems (2018). doi: 10.1109/TSMC.2018.2874942.
32.
LiuZ., QinK. and PeiZ., A method for fuzzy soft sets in decisionmaking based on an ideal solution, Symmetry9(10) (2017), 246. doi: 10.3390/sym9100246.
33.
MaX., ZhanJ., AliM.I. and MehmoodN., A survey of decision making methods based on two classes of hybrid soft set models, Artificial Intelligence Review (2016), forthcoming, doi: 10.1007/s10462-016-9534-2.
34.
MaX., LiuQ. and ZhanJ., A survey of decision making methods based on certain hybrid soft set models, Artificial Intelligence Review47 (2017), 507–530.
35.
MajiP.K., BiswasR. and RoyA.R., An application of soft sets in a decision-making problem, Computers and Mathematics with Applications44(8) (2002), 1077–1083.
36.
MajiP.K., BiswasR. and RoyA.R., Soft set theory, Computers and Mathematics with Applications45(4-5) (2003), 555–562.
37.
MajiP.K., BiswasR. and RoyA.R., Fuzzy soft sets, Journal of Fuzzy Mathematics9(3) (2001), 589–602.
38.
MolodtsovD.A., Soft set theory- First results, Computers and Mathematics with Applications37(4-5) (1999), 19–31.
39.
PawlakZ., Rough sets, International Journal of Computer and Information Sciences11(5) (1982), 145–172.
RoyA.R. and MajiP.K., A fuzzy soft set theoretic approach to decision making problems, Journal of Computational and Applied Mathematics203(2) (2007), 412–418.
42.
ZadehL.A., Fuzzy sets, Information and Control8(3) (1965), 338–353.
43.
ZhanJ. and AlcantudJ.C.R., A survey of parameter reduction of soft sets and corresponding algorithms, Artificial Intelligence Review, forthcoming.
44.
ZhangW.R., Bipolar fuzzy sets and relations: A computational framework for cognitive modeling and multi-agent decision analysis, Proc of IEEE Conf (1994), 305–309.
45.
ZhangH., DongY. and ChenX., The 2-rank consensus reaching model in the multigranular linguistic multiple-attribute group decision-making, IEEE Transactions on Systems, Man, and Cybernetics: Systems48(12) (2018), 2080–2094.
46.
ZhangH., DongY., ChiclanaF. and YuS., Consensus efficiency in group decision making: A comprehensive comparative study and its optimal design, European Journal of Operational Research275(2) (2019), 580–598.
47.
ZhangH., DongY., Palomares-CarrascosaI. and ZhouH., Failure mode and effect analysis in a linguistic context: A consensus-based multiattribute group decision-making approach, IEEE Transactions on Reliability (2018), in press. doi: 10.1109/TR.2018.2869787.
48.
ZouY. and XiaoZ., Data analysis approaches of soft sets under incomplete information, Knowledge-Based Systems21(8) (2008), 941–945.
