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

Abstract

Fuzzy set theory, rough set theory and soft set theory are all generic mathematical tools for dealing with uncertainties. There has been some progress concerning practical applications of these theories, especially, the use of these theories in decision making problems. In the present article, we review some decision making methods based on (fuzzy) soft sets, rough soft sets and soft rough sets. In particular, we provide several novel algorithms in decision making problems by combining these kinds of hybrid models. It may be served as a foundation for developing more complicated soft set models in decision making.

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References

  1. Acar U, Koyuncu F, Tanay B (2010) Soft sets and soft rings. Comput Math Appl 59(11):3458–3463

    MathSciNet  Article  MATH  Google Scholar 

  2. Acharjya DP, Das TK (2014) A decision making model using soft set and rough set on fuzzy approximation spaces. Int J Intell Syst Technol Appl 13:170–186

    Google Scholar 

  3. Akram M, Davvaz B, Feng F (2015) Fuzzy soft Lie algebras. J Multi-Value Log Soft Comput 24(5–6):501–520

  4. Aktas H, Cagman N (2007) Soft sets and soft groups. Inf Sci 177:2726–2735

    MathSciNet  Article  MATH  Google Scholar 

  5. Ali MI (2011) A note on soft sets, rough soft sets and fuzzy soft sets. Appl Soft Comput 11(4):3329–3332

    Article  Google Scholar 

  6. Ali MI, Feng F, Liu X, Shabir M (2009) On some new operations in soft set theory. Comput Math Appl 57(9):1547–1553

    MathSciNet  Article  MATH  Google Scholar 

  7. Arif Butt M, Akram M (2015) A novel fuzzy decision making system for cpu scheduling algorithm. Neural Comput Appl. doi:10.1007/s00521-015-1987-8

    Google Scholar 

  8. Ashraf A, Akram M, Sarwar SM (2014) Fuzzy decision support system for fertilizer. Neural Comput Appl 25(6):1495–1505

    Article  Google Scholar 

  9. Aygunoglu A, Aygun H (2009) Introduction to fuzzy soft groups. Comput Math Appl 58(6):1279–1286

    MathSciNet  Article  MATH  Google Scholar 

  10. Cagman N, Enginoglu S (2010) Soft matrix theory and its decision making. Comput Math Appl 59:3308–3314

    MathSciNet  Article  MATH  Google Scholar 

  11. Cagman N, Enginoglu S (2010) Soft set theory and uni-int decision making. Eur J Op Res 207(2):848–855

    MathSciNet  Article  MATH  Google Scholar 

  12. Cagman N, Citak F, Enginoglu S (2010) Fuzzy parameterized fuzzy soft set theory and its applications. Turk J Fuzzy Syst 1:21–35

    MATH  Google Scholar 

  13. Chen TY (2015) The inclusion-based topsis method with interval-valued intuitionistic fuzzy sets for multiple criteria group decision making. Appl Soft Comput 26:57–73

    Article  Google Scholar 

  14. Chen D, Tsang ECC, Yeung DS, Wang X (2005) The parameterization reduction of soft sets and its applications. Comput Math Appl 49(56):757–763

    MathSciNet  Article  MATH  Google Scholar 

  15. Deli I, Cagman N (2015) Intuitionistic fuzzy parameterized soft set theory and its decision making. Appl Soft Comput 28(4):109–113

    Article  Google Scholar 

  16. Feng F (2011) Soft rough sets applied to multicriteria group decision making. Ann Fuzzy Math Inf 2(1):69–80

    MathSciNet  MATH  Google Scholar 

  17. Feng F, Li YM (2013) Soft subsets and soft product operations. Inf Sci 232:44–57

    MathSciNet  Article  MATH  Google Scholar 

  18. Feng F, Jun YB, Zhao X (2008) Soft semirings. Comput Math Appl 56(10):2621–2628

    MathSciNet  Article  MATH  Google Scholar 

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

    MathSciNet  Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  21. 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 

  22. Feng F, Li YM, Cagman N (2012) Generalized uni-int decision making schemes based on choice value soft sets. Eur J Op Res 220:162–170

    MathSciNet  Article  MATH  Google Scholar 

  23. Feng F, Akram M, Davvaz B, Fotea VL (2014) Attribute analysis of information systems based on elementary soft implications. Knowl-Based Syst 70:281–292

    Article  Google Scholar 

  24. Han JS, Sun SA (2014) Applications of soft sets to \(q\)-ideals and \(a\)-ideals in \(BCI\)-algebras. J Comput Anal Appl 17(1):10–21

    MathSciNet  MATH  Google Scholar 

  25. Jun YB (2008) Soft \(BCK/BCI\)-algebras. Comput Math Appl 56(5):1408–1413

    MathSciNet  Article  MATH  Google Scholar 

  26. Jun YB, Park CH (2008) Applications of soft sets in ideal theory of \(BCK/BCI\)-algebras. Inf Sci 178(11):2466–2475

    MathSciNet  MATH  Google Scholar 

  27. Jun YB, Lee KJ, Park CH (2009) Soft set theory applied to ideals in \(d\)-algebras. Comput Math Appl 57(3):367–378

    MathSciNet  Article  MATH  Google Scholar 

  28. Jun YB, Lee KJ, Zhan J (2009) Soft \(p\)-ideals of soft \(BCI\)-algebras. Comput Math Appl 58(10):2060–2068

    MathSciNet  Article  MATH  Google Scholar 

  29. Jun YB, Song SZ, Sun SA, Sun SA (2014) Union soft sets applied to commutative \(BCI\)-ideals. J Comput Anal Appl 16(3):468–477

    MathSciNet  MATH  Google Scholar 

  30. Kalayathankal SJ, Singh GS (2010) A fuzzy soft flood alarm model. Math Comput Simul 80(5):887–893

    MathSciNet  Article  MATH  Google Scholar 

  31. Kong Z, Gao L, Wang L, Li S (2008) The normal parameter reduction of soft sets and its algorithm. Comput Math Appl 56(12):3029–3037

    MathSciNet  Article  MATH  Google Scholar 

  32. Kong Z, Gao L, Wang L (2009) Comment on “A fuzzy soft set theoretic approach to decision making problems”. J Comput Appl Math 223(2):540–542

    Article  MATH  Google Scholar 

  33. Kong Z, Zhang G, Wang L, Wu Z, Qi S, Wang H (2014) An efficient decision making approach in incomplete soft set. Appl Math Model 38(7–8):2141–2150

    MathSciNet  Article  Google Scholar 

  34. Liang D, Liu D (2015) A novel risk decision making based on decision-theoretic rough sets under hesitant fuzzy information. IEEE Trans Fuzzy Syst 23(2):237–247

    Article  Google Scholar 

  35. Li Z, Wen G, Han Y (2014) Decision making based on intuitionistic fuzzy soft sets and its algorithm. J Comput Anal Appl 17(4):620–631

    MathSciNet  MATH  Google Scholar 

  36. Maji PK, Biswas R, Roy AR (2001) Fuzzy soft sets. J Fuzzy Math 9(3):589–602

    MathSciNet  MATH  Google Scholar 

  37. Maji PK, Biswas R, Roy AR (2001) Intuitionistic fuzzy soft sets. J Fuzzy Math 9(3):677–692

    MathSciNet  MATH  Google Scholar 

  38. 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 

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

    MathSciNet  Article  MATH  Google Scholar 

  40. Maji PK, Roy AR, Biswas R (2004) On intuitionistic fuzzy soft sets. J Fuzzy Math 12(3):669–684

    MathSciNet  MATH  Google Scholar 

  41. Majumdar P, Samanta SK (2010) Generalised fuzzy soft sets. Comput Math Appl 59(4):1425–1432

    MathSciNet  Article  MATH  Google Scholar 

  42. Ma X, Zhan J (2014) Applications of a new soft set to \(h\)-hemiregular hemirings via \((M, N)-SI-h\)-ideals. J Intell Fuzzy Syst 26:2515–2525

    MathSciNet  MATH  Google Scholar 

  43. Ma X, Zhan J (2015) Applications of soft intersection set theory to \(h\)-hemiregular and \(h\)-semisimple hemirings. J Multi-Valued Log Soft Comput 25:105–124

    MathSciNet  Google Scholar 

  44. 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 

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

    MathSciNet  Article  MATH  Google Scholar 

  46. Nazmul S, Samanta SK (2014) Fuzzy soft topological groups. Fuzzy Inf Eng 6(1):71–92

    MathSciNet  Article  MATH  Google Scholar 

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

    MathSciNet  Article  MATH  Google Scholar 

  48. Qin K, Hong Z (2010) On soft equality. J Comput Appl Math 234(5):1347–1355

    MathSciNet  Article  MATH  Google Scholar 

  49. 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 

  50. Sahin R, Kucuk A (2015) Soft boolean algebra and its properties. J Comput Anal Appl 18:803–814

    MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  52. 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 

  53. Sun B, Ma W, Zhao H (2014) Decision-theoretic rough fuzzy set model and application. Inf Sci 283(5):180–196

    MathSciNet  Article  MATH  Google Scholar 

  54. Tao Z, Chen H, Song X, Zhou L, Liu J (2015) Uncertain linguistic fuzzy soft sets and their applications in group decision making. Appl Soft Comput 34:587–605

    Article  Google Scholar 

  55. Xiao Z, Gong K, Zou Y (2009) A combined forecasting approach based on fuzzy soft sets. J Comput Appl Math 228(1):326–333

    MathSciNet  Article  MATH  Google Scholar 

  56. Xu W, Ma J, Wang S, Hao G (2010) Vague soft sets and their properties. Comput Math Appl 59(2):787–794

    MathSciNet  Article  MATH  Google Scholar 

  57. Yang X, Lin TY, Yang J, Li Y, Yu D (2009) Combination of interval-valued fuzzy set and soft set. Comput Math Appl 58(3):521–527

    MathSciNet  Article  MATH  Google Scholar 

  58. Yao Y, Deng X (2014) Quantitative rough sets based on subsethood measures. Inf Sci 267(5):306–322

    MathSciNet  Article  MATH  Google Scholar 

  59. Yao Y, Mi J, Li Z (2014) A novel variable precision (\(\theta,\sigma \))-fuzzy rough set model based on fuzzy granules. Fuzzy Sets Syst 236:58–72

    MathSciNet  Article  MATH  Google Scholar 

  60. Yuksel S, Tozlu N, Dizman T (2015) An application of multicriteria group decision making by soft covering based rough sets. Filomat 29:209–219

    MathSciNet  Article  Google Scholar 

  61. Zadeh LA (1965) Fuzzy sets. Inf Control 8(65):338–353

    MathSciNet  Article  MATH  Google Scholar 

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

    Google Scholar 

  63. Zhan J, Dudek WA, Neggers J (2015) A new soft union set: characterizations of hemirings. Int J Mach Learn Cybern. doi:10.1007/s13042-015-0343-8

    Google Scholar 

  64. Zhan J, Liu Q, Zhu W (2016) Another approach to rough soft hemirings and decision making. Soft Comput. doi:10.1007/s00500-016-2058-5

    Google Scholar 

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

    MathSciNet  Article  MATH  Google Scholar 

  66. Zhang H, Shu L (2015) Generalized interval-valued fuzzy rough set and its application in decision making. Int J Fuzzy Syst 17:279–291

    MathSciNet  Article  Google Scholar 

  67. Zhang H, Shu L, Liao S (2014) Intuitionistic fuzzy soft rough set and its application in decision making. Abstr Appl Anal 2014(2):353–370

    MathSciNet  Google Scholar 

  68. 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 

  69. Zhu W (2009) Relationship among basic concepts in covering-based rough sets. Inf Sci 179(14):2478–2486

    MathSciNet  Article  MATH  Google Scholar 

  70. Zhu W, Wang S (2013) Rough matroids based on relations. Inf Sci 232(5):241–252

    MathSciNet  Article  MATH  Google Scholar 

  71. Zou Y, Xiao Z (2008) Data analysis approaches of soft sets under incomplete information. Knowl-Based Syst 21(8):941–945

    Article  Google Scholar 

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Acknowledgments

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 is partially supported by a Grant of National Natural Science Foundation of China (11561023; 11461025).

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Correspondence to Jianming Zhan.

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Ma, X., Liu, Q. & Zhan, J. A survey of decision making methods based on certain hybrid soft set models. Artif Intell Rev 47, 507–530 (2017). https://doi.org/10.1007/s10462-016-9490-x

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Keywords

  • Fuzzy set
  • Soft set
  • Rough set
  • Rough soft set
  • Soft rough set
  • Decision making

Mathematics Subject Classification

  • 03E72
  • 90B50
  • 06D72