Skip to main content
SpringerLink
Log in

Probabilistic soft sets and dual probabilistic soft sets in decision-making

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Since its introduction by Molodstov (Computers & Mathematics with Applications 37(4):19–31 1999), soft set theory has been widely applied in various fields of study. Soft set theory has also been combined with other theories like fuzzy sets theory, rough sets theory, and probability theory. The combination of soft sets and probability theory generates probabilistic soft set theory. However, decision-making based on the probabilistic soft set theory has not been discussed in the literature. In this paper, we propose new algorithms for decision-making based on the probabilistic soft set theory. An example to show the application of these algorithms is given, and its possible extensions and reinterpretations are discussed. Inspired by realistic situations, the notion of dual probabilistic soft sets is proposed, and also, its application in decision-making is investigated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

Notes

  1. Concerning the determination of weights, Liu et al. [31] and Winkler [41] provide arguments.

  2. Peng and Yang [36] is another recent reference on the applicability of regret theory to an extended model of soft sets with a stochastic component, namely, interval-valued fuzzy soft sets.

  3. Examples in Alcantud [2] show that when dominated alternatives are not eliminated, zero elements can appear at the C comparison matrix. For such reason, we cannot ensure a correct performance of the Perron-Frobenius argument for examples with dominated alternatives.

References

  1. Akram M, Shahzadi S (2016) Novel intuitionistic fuzzy soft multiple-attribute decision-making methods. Neural Comput & Applic 1–13

  2. Alcantud JCR (2015) Fuzzy soft set based decision making: a novel alternative approach. In: IFSA-EUSFLAT Conference 2015. Atlantic press, pp 106–111

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

    Article  Google Scholar 

  4. Alcantud JCR (2016) Fuzzy soft set decision making algorithms: some clarifications and reinterpretations. In: OL, et al. (ed.) Advances in artificial intelligence. 17th conference of the spanish association for artificial intelligence, CAEPIA 2016, Springer, pp 479–488

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

    Article  MathSciNet  MATH  Google Scholar 

  6. Alcantud JCR, Santos-García G (2017) A new criterion for soft set based decision making problems under incomplete information. Int J Comput Intell Syst 10:394–404

    Article  Google Scholar 

  7. Ali MI, Davvaz B, Shabir M (2012) Generalized fuzzy s-acts and their characterization by soft s-acts. Neural Comput & Applic 21(1):9–17

    Article  Google Scholar 

  8. Ali MI, Davvaz B, Shabir M (2013) Some properties of generalized rough sets. Inf Sci 224:170–179

    Article  MathSciNet  MATH  Google Scholar 

  9. Ali MI, Feng F, Liu X, Min WK, Shabir M (2009) On some new operations in soft set theory. Computers Mathematics with Applications 57(9):1547–1553

    Article  MathSciNet  MATH  Google Scholar 

  10. Atagün AO, Kamacı H, Oktay O (2016) Reduced soft matrices and generalized products with applications in decision making. Neural Comput & Applic 1–12

  11. Ċaġman N., ĊıTak F., Aktaṡ H. (2012) Soft int-group and its appli- cations to group theory. Neural Comput & Applic 21(1):151–158

    Google Scholar 

  12. Deli I, Eraslan S, ĊAġman N. (2016) ivnpiv-Neutrosophic soft sets and their decision making based on similarity measure. Neural Comput & Applic 1–17

  13. Farebrother RW (1988) Linear least squares computations. Marcel Dekker, Inc, New York

    MATH  Google Scholar 

  14. Feng F, Cho J, Pedrycz W, Fujita H, Herawan T (2016) Soft set based association rule mining. Knowl-Based Syst 111:268–282

    Article  Google Scholar 

  15. 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

    Article  MathSciNet  MATH  Google Scholar 

  16. Feng F, Jun YB, Zhao X (2008) Soft semirings. Computers & Mathematics with Applications 56 (10):2621–2628

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  18. Gunduz(Aras) C, Posul H (2016) On some new operations in probabilistic soft set theory. European Journal of Pure and Applied Mathematics 9(3):333–339

    MathSciNet  MATH  Google Scholar 

  19. Hakim F, Saari E, Herawan T (2014) On if-then multi soft sets-based decision making. In: L et al. (ed) Information and communication technology, no. 8407 in lecture notes in computer science. Springer, Berlin, pp 306–315

  20. Hakim F, Saari E, Herawan T (2014) Soft solution of soft set theory for recommendation in decision making. In: TH et al. (eds) Recent advances on soft computing and data mining, no. 287 in advances in intelligent systems and computing. Springer International Publishing, Switzerland, pp 313–324

  21. Han BH, Li X (2014) Propositional compilation for all normal parameter reductions of a soft set. Springer International Publishing, Cham, pp 184–193

    MATH  Google Scholar 

  22. Herawan T, Deris MM (2011) A soft set approach for association rules mining. Knowl-Based Syst 24 (1):186–195

    Article  Google Scholar 

  23. Herrero C (2014) An endogeneous scoring rule. Mimeo

  24. Jaynes E (2003) Probability theory: the logic of science, 2 edn. Cambridge University Press, New York

    Book  Google Scholar 

  25. Jiang Y, Tang Y, Chen Q, Liu H, Tang J (2010) Interval-valued intuitionistic fuzzy soft sets and their properties. Computers & Mathematics with Applications 60(3):906–918

    Article  MathSciNet  MATH  Google Scholar 

  26. Jun YB (2008) Soft bck/bci-algebras. Computers & Mathematics with Applications 56(5):1408–1413

    Article  MathSciNet  MATH  Google Scholar 

  27. Jun YB, Park CH (2008) Applications of soft sets in ideal theory of bck/bci-algebras. Inform Sci 178 (11):2466–2475

    MathSciNet  MATH  Google Scholar 

  28. Kong Z, Wang L, Wu Z (2011) Application of fuzzy soft set in decision making problems based on grey theory. J Comput Appl Math 236(6):1521–1530

    Article  MathSciNet  Google Scholar 

  29. 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

    Article  MathSciNet  MATH  Google Scholar 

  30. Krugman P, Wells R, Graddy K (2011) Essentials of economics, 2 edn. Worth, New York

    Google Scholar 

  31. Liu X, Ghorpade A, Tu Y, Zhang W (2012) A novel approach to probability distribution aggregation. Inf Sci 188:269–275

    Article  Google Scholar 

  32. Ma X, Liu Q, Zhan J (2016) A survey of decision making methods based on certain hybrid soft set models. Artif Intell Rev 1–24

  33. Maji P, Roy A, Biswas R (2002) An application of soft sets in a decision making problem. Computers & Mathematics with Applications 44(8):1077–1083

    Article  MathSciNet  MATH  Google Scholar 

  34. Molodtsov D (1999) Soft set theory—first results. Computers & Mathematics with Applications 37(4):19–31

    Article  MathSciNet  MATH  Google Scholar 

  35. Peng X, Yang Y (2015) Approaches to interval-valued intuitionistic hesitant fuzzy soft sets based decision making. Annals of Fuzzy Mathematics and Informatics 10(4):657–680

    MathSciNet  MATH  Google Scholar 

  36. Peng X, Yang Y (2016) Algorithms for interval-valued fuzzy soft sets in stochastic multi-criteria decision making based on regret theory and prospect theory with combined weight. Applied Soft Computing p. in press

  37. Poncela-Casasnovas J, Gutiérrez-Roig M, Gracia-Lázaro C, Vicens J, Gómez-Gardeñes J, Perelló J, Moreno Y, Duch J, Sánchez A (2016) Humans display a reduced set of consistent behavioral phenotypes in dyadic games 2(8). doi:10.1126/sciadv.1600451 10.1126/sciadv.1600451

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  40. Savage L The theory of statistical decision. J Am Stat Assoc 46

  41. Winkler RL (1968) The consensus of subjective probability distributions. Manag Sci 15(2):B61–B75

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  43. Xu W, Ma J, Wang S, Hao G (2010) Vague soft sets and their properties. Computers and Mathematics with Applications 59:787–794

    Article  MathSciNet  MATH  Google Scholar 

  44. 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 63:59–67

    Article  Google Scholar 

  45. Yager RR (2017) OWA aggregation of probability distributions using the probabilistic exceedance method. Springer International Publishing, Cham, pp 277–289

    Google Scholar 

  46. Yang Z, Chen Y (2013) Fuzzy soft set-based approach to prioritizing technical attributes in quality function deployment. Neural Comput & Applic 23(7):2493–2500

    Article  Google Scholar 

  47. Zhan J, Liu Q, Herawan T (2016) A novel soft rough set: soft rough hemirings and corresponding multicriteria group decision making. Applied soft computing p. in press

  48. Zhan J, Liu Q, Zhu W (2016) Another approach to rough soft hemirings and corresponding decision making. Soft Comput pp 1–12

  49. Zhang Hd, Shu L (2016) Dual hesitant fuzzy soft set and its properties. Springer International Publishing, Cham, pp 171–182

    MATH  Google Scholar 

  50. Zhu P, Wen Q (2010) Probabilistic soft sets. IEEE International Conference on Granular Computing 51:635–638

    Google Scholar 

Download references

Acknowledgments

Part of this research was done while the first author was invited at the Department of Economics and Economic History in Salamanca. Their hospitality is gratefully acknowledged. The authors are thankful to the Editor-in-Chief, Professor John MacIntyre, and the anonymous referees for their time and efforts to review this article.

Author information

Authors and Affiliations

  1. Department of Mathematics, Universitas Gadjah Mada, Yogyakarta, Indonesia

    Fatia Fatimah & Dedi Rosadi

  2. Department of Mathematics, Universitas Terbuka, South Tangerang, Indonesia

    Fatia Fatimah

  3. Department of Statistics, Universitas Islam Indonesia, Yogyakarta, Indonesia

    RB. Fajriya Hakim

  4. BORDA Research Unit and IME, University of Salamanca, 37007, Salamanca, Spain

    José Carlos R. Alcantud

Authors
  1. Fatia Fatimah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dedi Rosadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. RB. Fajriya Hakim
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. José Carlos R. Alcantud
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fatia Fatimah.

Ethics declarations

Conflict of interests

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fatimah, F., Rosadi, D., Hakim, R.F. et al. Probabilistic soft sets and dual probabilistic soft sets in decision-making. Neural Comput & Applic 31 (Suppl 1), 397–407 (2019). https://doi.org/10.1007/s00521-017-3011-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-017-3011-y

Keywords

Search

Navigation