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Artificial Intelligence Review

, Volume 52, Issue 3, pp 1839–1872 | Cite as

A survey of parameter reduction of soft sets and corresponding algorithms

  • Jianming ZhanEmail author
  • José Carlos R. Alcantud
Article

Abstract

As is well known, soft set theory can have a bearing on making decisions in many fields. Particularly important is parameter reduction of soft sets, an essential topic both for information sciences and artificial intelligence. Parameter reduction studies the largest pruning of the amount of parameters that define a given soft set without changing its original choice objects. Therefore it can spare computationally costly tests in the decision making process. In the present article, we review some different algorithms of parameter reduction based on some types of (fuzzy) soft sets. Finally, we compare these algorithms to emphasize their respective advantages and disadvantages, and give some examples to illustrate their differences.

Keywords

Parameter reduction Normal parameter reduction Soft set Fuzzy soft set Decision making 

Notes

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 and 11561023).

References

  1. Aktas H, Çağman N (2007) Soft sets and soft groups. Inf Sci 177:2726–2735MathSciNetzbMATHGoogle Scholar
  2. Alcantud JCR (2015) Fuzzy soft set based decision making: a novel alternative approach. In: Alonso JM, Bustince H, Reformat M (eds) Proceedings of the 2015 conference of the international fuzzy systems association and the European society for fuzzy logic and technology. Atlantis PressGoogle Scholar
  3. Alcantud JCR (2016) A novel algorithm for fuzzy soft set based decision making from multiobserver input parameter data set. Inform Fusion 29:142–148Google Scholar
  4. Alcantud JCR (2016) Some formal relationships among soft sets, fuzzy sets and their extensions. Int J Approx Reason 68:45–53MathSciNetzbMATHGoogle Scholar
  5. Alcantud JCR (2016) Fuzzy soft set decision making algorithms: some clarifications and reinterpretations. In: Rodríguez O Luaces et al (eds) Advances in artificial intelligence. 17th Conference of the Spanish association for artificial intelligence, CAEPIA 2016, lecture notes in artificial intelligence, vol 9868, pp 479–488. SpringerGoogle Scholar
  6. Alcantud JCR, Mathew TJ (2017) Separable fuzzy soft sets and decision making with positive and negative attributes. Appl Soft Comput 59:586–595Google Scholar
  7. Alcantud JCR, Santos-García G (2017) A new criterion for soft set based decision making problems under incomplete information. Int J Comput Intell Syst 10:394–404Google Scholar
  8. Alcantud JCR, Santos-García G, Hernández-Galilea E (2015) Glaucoma diagnosis: a soft set based decision making procedure. In: Puerta JM, Gámez JA, Dorronsoro B, Barrenechea E, Troncoso A, Baruque B, Galar M (eds) Advances in artificial intelligence. 16th Conference of the Spanish association for artificial intelligence, CAEPIA 2015, lecture notes in artificial intelligence. SpringerGoogle Scholar
  9. Ali MI (2011) A note on soft sets, rough sets and fuzzy soft sets. Appl Soft Comput 11(4):3329–3332Google Scholar
  10. Ali MI (2012) Another view on reduction of parameters in soft sets. Appl Soft Comput 12(6):1814–1821Google Scholar
  11. Ali MI, Feng F, Liu X, Min WK, Shabir M (2009) On some new operations in soft set theory. Comput Math Appl 57(9):1547–1553MathSciNetzbMATHGoogle Scholar
  12. Ali MI, Shabir M (2014) Logic connectives for soft sets and fuzzy soft sets. IEEE Trans Fuzzy Syst 22(6):1431–1442Google Scholar
  13. Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96zbMATHGoogle Scholar
  14. Bakshi T, Sinharay A, Som T (2016) An introduction towards automated parameterization reduction of soft set. In: Recent advances in information technology (RAIT), 2016 3rd international conference on IEEEGoogle Scholar
  15. Basu TM, Mahapatra NK, Mondal SK (2012) A balanced solution of a fuzzy soft set based decision making problem in medical science. Appl Soft Comput 12(10):3260–3275Google Scholar
  16. Bonikowski Z, Bryniarski E, Wybraniec-Skardowska U (1998) Extensions and intentions in rough set theory. Inf Sci 107:149–167MathSciNetzbMATHGoogle Scholar
  17. Çağman N, Enginoğlu S (2010) Soft matrix theory and its decision making. Comput Math Appl 59:3308–3314MathSciNetzbMATHGoogle Scholar
  18. Çağman N, Enginoğlu S (2010) Soft set theory and uni–int decision making. Eur J Oper Res 207(2):848–855MathSciNetzbMATHGoogle Scholar
  19. Chen D, Li W, Zhang X, Kwong S (2014) Evidence-theory-based numerical algorithms of attribute reduction with neighborhood-covering rough sets. Int J Approx Reason 55:908–923MathSciNetzbMATHGoogle Scholar
  20. Chen D, Tsang ECC, Yeung DS, Wang X (2005) The parameterization reduction of soft sets and its applications. Comput Math Appl 49(56):757–763MathSciNetzbMATHGoogle Scholar
  21. Danjuma S, Herawan T, Ismail MA, Chiroma H, Abubakar AI, Zeki AM (2017) A review on soft set-based parameter reduction and decision making. IEEE Access 5:4671–4689Google Scholar
  22. Danjuma S, Ismail MA, Herawan T (2017) An alternative approach to normal parameter reduction algorithm for soft set theory. IEEE Access 5:4732–4746Google Scholar
  23. Deli I, Çağman N (2015) Intuitionistic fuzzy parameterized soft set theory and its decision making. Appl Soft Comput 28(4):109–113Google Scholar
  24. Deng T, Wang X (2012) Parameter significance and reductions of soft sets. Int J Comput Math 89(15):1–17MathSciNetzbMATHGoogle Scholar
  25. Dubois D, Prade H (1990) Rough fuzzy sets and fuzzy rough sets. Int J Gen Syst 17:191–209zbMATHGoogle Scholar
  26. 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):10–20MathSciNetzbMATHGoogle Scholar
  27. Feng F, Jun YB, Zhao X (2008) Soft semirings. Comput Math Appl 56(10):2621–2628MathSciNetzbMATHGoogle Scholar
  28. 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):899–911zbMATHGoogle Scholar
  29. Feng F, Li Y, Leoreanu-Fotea V (2010) Application of level soft sets in decision making based on interval-valued fuzzy soft sets. Comput Math Appl 60(6):1756–1767MathSciNetzbMATHGoogle Scholar
  30. Feng F, Liu XY, Leoreanu-Fotea V, Jun YB (2011) Soft sets and soft rough sets. Inf Sci 181(6):1125–1137MathSciNetzbMATHGoogle Scholar
  31. Gong K, Wang P, Peng Y (2017) Fault-tolerant enhanced bijective soft set with applications. Appl Soft Comput 54:431–439Google Scholar
  32. Gong K, Wang P, Xiao Z (2013) Bijective soft set decision system based parameters reduction under fuzzy environments. Appl Math Model 37:4474–4485MathSciNetzbMATHGoogle Scholar
  33. Gong K, Xiao Z, Zhang X (2010) The bijective soft set with its operations. Comput Math Appl 60:2270–2278MathSciNetzbMATHGoogle Scholar
  34. Guan Y, Wang H (2006) Set-valued information systems. Inf Sci 176:2507–2525MathSciNetzbMATHGoogle Scholar
  35. Han BH (2016) Comments on “Normal parameter reduction in soft set based on particle swarm optimization algorithm”. Appl Math Model 40(23–24):10828–10834MathSciNetGoogle Scholar
  36. Han BH, Li YM, Geng SL (2017) 0–1 Linear programming methods for optimal normal and pseudo parameter reductions of soft sets. Appl Soft Comput 54:467–484Google Scholar
  37. Han BH, Li YM, Liu J, Geng SL, Li H (2014) Elicitation criterions for restricted intersection of two incomplete soft sets. Knowl Based Syst 59:121–131Google Scholar
  38. Herawan T, Deris MM (2011) A soft set approach for association rules mining. Knowl Based Syst 24(1):186–195Google Scholar
  39. Jiang Y, Liu H, Tang Y, Chen Q (2011) Semantic decision-making using ontology based soft sets. Math Comput Modell 53:1140–1149MathSciNetzbMATHGoogle Scholar
  40. Jiang Y, Tang Y, Chen Q (2011) An adjustable approach to intuitionistic fuzzy soft sets based decision making. Appl Math Model 35(2):824–836MathSciNetzbMATHGoogle Scholar
  41. Jun YB, Park CH (2008) Applications of soft sets in ideal theory of BCK/BCI-algeras. Inf Sci 178(11):2466–2475zbMATHGoogle Scholar
  42. Karaaslan F (2017) Possibility neutrosophic soft sets and PNS-decision making method. Appl Soft Comput 54:403–414Google Scholar
  43. Kim YK, Min WK (2014) Full soft sets and full soft decision systems. J Intell Fuzzy Syst 26(2):925–933MathSciNetzbMATHGoogle Scholar
  44. Khan MS, Herawan T, Wahab AWA, Mujtaba G, Al-Garadi MA (2017) Concept of entire Boolean values recalculation from aggregates in the preprocessed category of incomplete soft sets. IEEE Access 5:11444–11454Google Scholar
  45. Khan MS, Al-Garadi MA, Wahab AWA, Herawan T (2016) An alternative data filling approach for prediction of missing data in soft sets (ADFIS). Springerplus 5(1):1348Google Scholar
  46. Kong Z, Gao L, Wang L (2007) Comment on “A fuzzy soft set theoretic approach to decision making problems”. J Comput Appl Math 223:540–542zbMATHGoogle Scholar
  47. Kong Z, Gao L, Wang L, Li S (2008) The normal parameter reduction of soft sets and its algorithm. Comput Math Appl 56(12):3029–3037MathSciNetzbMATHGoogle Scholar
  48. Kong Z, Jia W, Zhang G, Wang L (2015) Normal parameter reduction in soft set based on particle swarm optimization algorithm. Appl Math Model 39:4808–4820MathSciNetGoogle Scholar
  49. Kumar SU, Inbarani HH, Kumar SS (2013) Bijective soft set based classification of medical data. In: Proceedings of the 2013 international conference on pattern recognition, informatics and mobile engineering, PRIME 2013, Article number 6496725, pp 517–521Google Scholar
  50. Li Z, Gao N, Zhang G (2014) New methods on parameter reduction of soft sets. Control Decis 29(7):1285–1290Google Scholar
  51. Li J, Kumar CA, Mei C, Wang X (2017) Comparison of reduction in formal decision contexts. Int J Approx Reason 80:100–122MathSciNetzbMATHGoogle Scholar
  52. Li Z, Wen G, Han Y (2014) Decision making based on intuitionistic fuzzy soft sets and its algorithm. J Comput Anal Appl 17(4):620–631MathSciNetzbMATHGoogle Scholar
  53. Li Z, Wen G, Xie N (2015) An approach to fuzzy soft sets in decision making based on grey relational analysis and Dempster–Shafer theory of evidence: an application in medical diagnosis. Artif Intell Med 64(3):161–171Google Scholar
  54. Li Z, Xie N, Wen G (2015) Soft coverings and their parameter reductions. Appl Soft Comput 31:48–60Google Scholar
  55. Ma X, Liu Q, Zhan J (2017) A survey of decision making methods based on certain hybrid soft set models. Artif Intell Rev 47:507–530Google Scholar
  56. Ma X, Sulaiman N, Qin H, Herawan T, Zain JM (2011) A new efficient normal parameter reduction algorithm of soft sets. Comput Math Appl 62:588–598MathSciNetzbMATHGoogle Scholar
  57. Maji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45(4):555–562MathSciNetzbMATHGoogle Scholar
  58. Maji PK, Roy AR, Biswas R (2002) An application of soft sets in a decision making problem. Comput Math Appl 44(8):1077–1083MathSciNetzbMATHGoogle Scholar
  59. Maji PK, Roy AR, Biswas R (2001) Fuzzy soft sets. J Fuzzy Math 9(3):589–602MathSciNetzbMATHGoogle Scholar
  60. Mathew TJ, Sherly E, Alcantud JCR (2018) An adaptive soft set based diagnostic risk prediction system. In: Thampi SM et al (eds) Intelligent systems technologies and applications, chapter 13. Advances in intelligent systems and computing, vol 683. Springer International Publishing AG, Cham.  https://doi.org/10.1007/978-3-319-68385-0_13 Google Scholar
  61. Meng D, Zhang X, Qin K (2011) Soft rough fuzzy sets and soft fuzzy rough sets. Comput Math Appl 62(12):4635–4645MathSciNetzbMATHGoogle Scholar
  62. Miao B, Wei W (2012) The parameter reduction algorithm and its application in decision-making based on the bijective soft set. Syst Eng 30:115–119Google Scholar
  63. Moghaddam MA, Golmezergi R, Kolahan F (2016) Multi-variable measurements and optimization of GMAW parameters for API-X42 steel alloy using a hybrid BPNNVPSO approach. Measurement 92:279–287Google Scholar
  64. Mohamad M, Selamat A (2016) A new hybrid rough set and soft set parameter reduction method for spam e-mail classification task. In: Part Ohwada H, Yoshida K (eds) 14th Pacific rim knowledge acquisition workshop, PKAW 2016, Phuket, Thailand, August 22–23, 2016, Proceedings. Springer, BerlinGoogle Scholar
  65. Molodtsov D (1999) Soft set theory-first results. Comput Math Appl 37(4):19–31MathSciNetzbMATHGoogle Scholar
  66. Molodtsov D (2004) The theory of soft sets. URSS Publishers, Moscow (in Russion)Google Scholar
  67. Nozdrzykowski L, Nozdrzykowska M (2018) Testing the significance of parameters of models estimating execution time of parallel program loops according to the Open MPI Standard. In: Zamojski W, Mazurkiewicz J, Sugier J, Walkowiak T, Kacprzyk J (eds) Advances in dependability engineering of complex systems. DepCoS-RELCOMEX 2017. Advances in intelligent systems and computing, vol 582. Springer, ChamGoogle Scholar
  68. Pawlak Z (1982) Rough sets. Int J Comput Inform Sci 11(5):341–356zbMATHGoogle Scholar
  69. Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data. Kluwer Academic, BostonzbMATHGoogle Scholar
  70. Peng XD, Dai JG (2017) Hesitant fuzzy soft decision making methods based on WASPAS, MABAC and COPRAS with combined weights. J Intell Fuzzy Syst 33:1313–1325zbMATHGoogle Scholar
  71. Peng XD, Dai JG, Yuan HY (2017) Interval-valued fuzzy soft decision making methods based on MABAC, similarity measure and EDAS. Fund Inform 152:373–396MathSciNetzbMATHGoogle Scholar
  72. Peng XD, Liu C (2017) Algorithms for neutrosophic soft decision making based on EDAS, new similarity measure and level soft set. J Intell Fuzzy Syst 32:955–968zbMATHGoogle Scholar
  73. Peng XD, Yang Y (2017) Algorithms for interval-valued fuzzy soft sets in stochastic multi-criteria decision making based on regret theory and prospect theory with combined weight. Appl Soft Comput 54:415–430Google Scholar
  74. Qian J, Miao DQ, Zhang ZH, Li W (2011) Hybrid approaches to attribute reduction based on indiscernibility and discernibility relation. Int J Approx Reason 52:212–230MathSciNetzbMATHGoogle Scholar
  75. Rose ANM, Herawan T, Deris MM (2010) A framework of decision making based on maximal supported sets. In: Zhang L, Lu B-L, Kwok J (eds) Advances in neural networks—ISNN 2010: 7th international symposium on neural networks, ISNN 2010, Shanghai, China, June 6–9, 2010, Proceedings, Part I. Springer, BerlinGoogle Scholar
  76. Roy AR, Maji PK (2007) A fuzzy soft set theoretic approach to decision making problems. J Comput Appl Math 203(2):412–418zbMATHGoogle Scholar
  77. Shabir M, Ali MI, Shaheen T (2013) Another approach to soft rough sets. Knowl Based Syst 40(1):72–80Google Scholar
  78. Sun B, Ma W (2014) Soft fuzzy rough sets and its application in decision making. Artif Intell Rev 41(1):67–80Google Scholar
  79. Sun B, Ma W (2016) An approach to evaluation of emergency plans for unconventional emergency events baased on soft fuzzy rough set. Kybernetes 45:461–473MathSciNetGoogle Scholar
  80. Sun B, Ma W, Li XN (2017) Linguistic value soft set-based approach to multiple criteria group decision-making. Appl Soft Comput 58:285–296Google Scholar
  81. Sun B, Ma W, Xiao X (2017) Three-way group decision making based on multigranulation fuzzy decision-theoretic rough set over two universes. Int J Approx Reason 81:87–102MathSciNetzbMATHGoogle Scholar
  82. Sun B, Ma W, Zhao H (2014) Decision-theoretic rough fuzzy set model and application. Inf Sci 283(5):180–196MathSciNetzbMATHGoogle Scholar
  83. Tang H (2015) A novel fuzzy soft set approach in decision making based on grey relational analysis and Dempster–Shafer theory of evidence. Appl Soft Comput 31:317–325Google Scholar
  84. Taş N, Özgür NY, Demir P (2017) An application of soft set and fuzzy soft set theories to stock management. J Nat Appl Sci (forthcoming) Google Scholar
  85. Wang G, Ma X, Yu H (2015) Monotonic uncertainty measures for attribute reduction in probabilistic rough set model. Int J Approx Reason 59:41–67MathSciNetzbMATHGoogle Scholar
  86. Xiao Z, Gong K, Li D (2011) Bijective soft set decision system based parameters reduction. Syst Eng Theory Pract 31(2):308–314Google Scholar
  87. Xiao Z, Gong K, Xia S, Zou Y (2010) Exclusive disjunctive soft sets. Comput Math Appl 59(6):2128–2137MathSciNetzbMATHGoogle Scholar
  88. Xie NX (2016) An algorithm on the parameter reduction of soft sets. Fuzzy Inform Eng 8:127–145MathSciNetGoogle Scholar
  89. Xu W, Xiao Z, Dang X, Yang D, Yang X (2014) Financial ratio selection for business failure prediction using soft set theory. Knowl Based Syst 63:59–67Google Scholar
  90. Yang Y, Peng XD (2017) A revised TOPSIS method based on interval fuzzy soft set models with incomplete weight information. Fund Inform 152:297–321MathSciNetzbMATHGoogle Scholar
  91. Yao YY (2010) Three-way decisions with probabilistic rough sets. Inform Sci 180:341–353MathSciNetGoogle Scholar
  92. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353zbMATHGoogle Scholar
  93. Zhan J (2015) The uncertainties of ideal theory on hemirings. Science Press, BeijingGoogle Scholar
  94. Zhan J, Liu Q, Davvaz B (2015) A new rough set theory: rough soft hemirings. J Intell Fuzzy Syst 28:1687–1697MathSciNetzbMATHGoogle Scholar
  95. Zhan J, Ali M, Mehmood N (2017) On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods. Appl Soft Comput 56:446–457Google Scholar
  96. Zhan J, Liu Q, Zhu W (2017) Another approach to rough soft hemirings and corresponding decision making. Soft Comput 21:3769–3780zbMATHGoogle Scholar
  97. Zhan J, Zhu K (2017) A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making. Soft Comput 21:19231936zbMATHGoogle Scholar
  98. Zhan J, Zhu K (2015) Reviews on decision making methods based on (fuzzy) soft sets and rough soft sets. J Intell Fuzzy Syst 29:1169–1176MathSciNetzbMATHGoogle Scholar
  99. Zhang G, Li Z, Qin B (2016) A method for multi-attribute decision making applying soft rough sets. J Intell Fuzzy Syst 30:1803–1815zbMATHGoogle Scholar
  100. Zhang G, Xie N, Li Z (2017) Parameter reductions of soft equivalence relations. Int J Mach Learn Cybernet 8:711–720Google Scholar
  101. Zhang Q, Wang X (2016) A new parameter reduction method based on soft set theory. Int J Hybrid Inform Technol 9:99–108Google Scholar
  102. Zhang W, Wu W, Liang J (2001) Rough sets theory and methods. Science Press, BeijingGoogle Scholar
  103. Zhang XH, Miao D, Liu C, Le M (2016) Constructive methods of rough approximation operators and multigranuation rough sets. Knowl Based Syst 91:114–125Google Scholar
  104. Zhang Z (2012) A rough set approach to intuitionistic fuzzy soft sets based decision making. Appl Math Model 36(10):4605–4633MathSciNetzbMATHGoogle Scholar
  105. Zhang Z (2013) The parameter reduction of fuzzy soft sets based on soft fuzzy rough sets. Adv Fuzzy Syst 2013:1–12Google Scholar
  106. 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):1255–1270MathSciNetzbMATHGoogle Scholar
  107. Zhu W (2007) Generalized rough sets based on relations. Inf Sci 177(22):4997–5011MathSciNetzbMATHGoogle Scholar
  108. Zou Y, Xiao Z (2008) Data analysis approaches of soft sets under incomplete information. Knowl Based Syst 21(8):941–945Google Scholar

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Authors and Affiliations

  1. 1.Department of MathematicsHubei University for NationalitiesEnshiPeople’s Republic of China
  2. 2.BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME)University of SalamancaSalamancaSpain

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