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A survey of decision making methods based on two classes of hybrid soft set models

Abstract

To the best of our knowledge, the tool of soft set theory is a new efficacious technique to dispose uncertainties and it focuses on the parameterization, while fuzzy set theory emphasizes the truth degree and rough set theory as another tool to handle uncertainties, it places emphasis on granular. However, the real-world problems that under considerations are usual very complicated. Consequently, it is very difficult to solve them by a single mathematical tool. It is worth noting that decision making (briefly, DM) in an imprecise environment has been showing more and more role in real-world applications. Researches on the idiographic applications of the above three uncertain theories as well as their hybrid models in DM have attracted many researchers’ widespread interest. DM methods are not yet proposed based on fusions of the above three uncertain theories. In view of the reason, by compromising the above three uncertain theories, we elaborate some reviews to DM methods based on two classes of hybrid soft models: SRF-sets and SFR-sets. We test all algorithms for DM and computation time on data sets produced by soft sets and FS-sets. The numerical experimentation programs are written for given pseudo codes in MATLAB. At the same time, the comparisons of all algorithms are given. Finally, we expatiate on an overview of techniques based on the involved hybrid soft set models.

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References

  • Ali MI (2011) A note on soft sets, rough sets and fuzzy soft sets. Appl Soft Comput 11:3329–3332

    Article  Google Scholar 

  • Ali MI (2012) Another view on reduction of parameters in soft sets. Appl Soft Comput 12:1814–1821

    Article  Google Scholar 

  • Ali MI, Shabir M (2014) Logic connectives for soft sets and fuzzy soft sets. IEEE Trans Fuzzy Syst 22(6):1431–1442

    Article  Google Scholar 

  • Alcantud JCR (2016a) A novel algorithm for fuzzy soft set based decision making from multiobserver input parameter data set. Inf Fusion 29:142–148

    Article  Google Scholar 

  • Alcantud JCR (2016b) Some formal relationships among soft sets, fuzzy sets and their extensions. Int J Approx Reason 68:45–53

    MathSciNet  Article  MATH  Google Scholar 

  • Çağman N, Enginoğlu S (2010a) Soft matrix theory and its decision making. Comput Math Appl 59:3308–3314

    MathSciNet  Article  MATH  Google Scholar 

  • Çağman N, Enginoğlu S (2010b) Soft set theory and uni-int decision making. Eur J Oper Res 207:848–855

    MathSciNet  Article  MATH  Google Scholar 

  • Feng F, Jun YB, Liu X, Li L (2010a) An adjustable approach to fuzzy soft set based decision making. J Comput Appl Math 234(1):10–20

    MathSciNet  Article  MATH  Google Scholar 

  • Feng F, Li C, Davvaz B, Ali MI (2010b) Soft sets combined with fuzzy sets and rough sets: a tentative approach. Soft Comput 14(9):899–911

    Article  MATH  Google Scholar 

  • Feng F, Li Y, Leoreanu-Fotea V (2010c) Application of level soft sets in decision making based on interval-valued fuzzy soft sets. Comput Math Appl 60(6):1756–1767

    MathSciNet  Article  MATH  Google Scholar 

  • Feng F, Liu XY, Leoreanu-Fotea V, Jun YB (2011) Soft sets and soft rough sets. Inf Sci 181(6):1125–1137

    MathSciNet  Article  MATH  Google Scholar 

  • Jiang Y, Tang Y, Chen Q (2011) An adjustable approach to intuitionistic fuzzy soft sets based decision making. Appl Math Model 35(2):824–836

    MathSciNet  Article  MATH  Google Scholar 

  • Kong Z, Gao LQ, Wang LF (2007) Comment on “A fuzzy soft set theoretic approach to decision making problems”. J Comput Math Appl 223:540–542

    Article  MATH  Google Scholar 

  • Kong Z, Zhang G, Wang L (2014) An efficient decision making approach in incomplete soft set. Appl Math Model 38(7):2141–2150

    MathSciNet  Article  Google Scholar 

  • Li Z, Xie T (2014) The relationship among soft sets, soft rough sets and topologies. Soft Comput 18:717–728

    Article  MATH  Google Scholar 

  • Li Z, Xie N, Wen G (2015) Soft coverings and their parameter reductions. Appl Soft Comput 31:48–60

    Article  Google Scholar 

  • Ma X, Liu Q, Zhan J (2016) A survey of decision making methods based on certain hyperid soft set models. Artif Intell Rev. doi:10.1007/s10462-016-9490-X

    Google Scholar 

  • Maji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45(4):555–562

    MathSciNet  Article  MATH  Google Scholar 

  • Maji PK, Roy AR, Biswas R (2002) An application of soft sets in a decision making problem. Comput Math Appl 44(8):1077–1083

    MathSciNet  Article  MATH  Google Scholar 

  • Meng D, Zhang X, Qin K (2011) Soft rough fuzzy sets and soft fuzzy rough sets. Comput Math Appl 62(12):4635–4645

    MathSciNet  Article  MATH  Google Scholar 

  • Molodtsov D (1999) Soft set theory-first results. Comput Math Appl 37(4):19–31

    MathSciNet  Article  MATH  Google Scholar 

  • Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11(5):341–356

    Article  MATH  Google Scholar 

  • Roy AR, Maji PK (2007) A fuzzy soft set theoretic approach to decision making problems. J Comput Appl Math 203(2):412–418

    Article  MATH  Google Scholar 

  • Shabir M, Ali MI, Shaheen T (2013) Another approach to soft rough sets. Knowl Based Syst 40(1):72–80

    Article  Google Scholar 

  • Sun B, Ma W (2013) An approach to decision making based on intuitionistic fuzzy rough set over two universes. J Oper Res Soc 64(7):1079–1089

    Article  Google Scholar 

  • Sun B, Ma W (2014) Soft fuzzy rough sets and its application in decision making. Artif Intell Rev 41(1):67–80

    Article  Google Scholar 

  • Sun B, Ma W (2016) An approach to evaluation of emergency plans for unconventional emergency events based on soft fuzzy rough set. Kybernetes 45:461–473

    MathSciNet  Article  Google Scholar 

  • Yao YY (2010) Three-way decisions with probabilistic rough sets. Inf Sci 180:341–353

    MathSciNet  Article  Google Scholar 

  • Zhan J (2015) The uncertainties of ideal theory on hemirings. Science Press, Beijing

    Google Scholar 

  • Zhan J, Zhu K (2015) Reviews on decision making methods based on (fuzzy) soft sets and rough soft sets. J Intell Fuzzy Syst 29:1169–1176

    MathSciNet  Article  MATH  Google Scholar 

  • Zhan J, Zhu K (2016) A novel soft rough fuzzy set: \(Z\)-soft rough fuzzy ideals of hemirings and corresponding decision making. Soft Comput. doi:10.1007/s00500-016-2119-9

    MATH  Google Scholar 

  • Zhan J, Liu Q, Davvaz B (2015) A new rough set theory: rough soft hemirings. J Intell Fuzzy Syst 28:1687–1697

    MathSciNet  MATH  Google Scholar 

  • Zhang Z (2012) A rough set approach to intuitionistic fuzzy soft sets based decision making. Appl Math Model 36(10):4605–4633

    MathSciNet  Article  MATH  Google Scholar 

  • Zhang Z, Wang C, Tian D (2014) A novel approach to interval-valued intuitionistic fuzzy soft sets based decision making. Appl Math Model 38(4):1255–1270

    MathSciNet  Article  Google Scholar 

  • Zhang XH, Miao D, Liu C, Le M (2016) Constructive methods of rough approximation operators and multigranuation rough sets. Knowl Based Syst 91:114–125

    Article  Google Scholar 

  • Zhu W (2007) Generalized rough sets based on relations. Inform Sci 177(22):4997–5011

    MathSciNet  Article  MATH  Google Scholar 

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Acknowledgements

The authors are extremely grateful to the editor and the referees for their valuable comments and helpful suggestions which help to improve the presentation of this paper. This research was supported by NNSFC (11461025; 11561023).

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Correspondence to Jianming Zhan.

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Ma, X., Zhan, J., Ali, M.I. et al. A survey of decision making methods based on two classes of hybrid soft set models. Artif Intell Rev 49, 511–529 (2018). https://doi.org/10.1007/s10462-016-9534-2

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  • DOI: https://doi.org/10.1007/s10462-016-9534-2

Keywords

  • Soft set
  • SRF-set
  • SFR-set
  • DM method