Skip to main content
SpringerLink
Log in

A new parameter reduction algorithm for interval-valued fuzzy soft sets based on Pearson’s product moment coefficient

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

Interval-valued fuzzy soft set theory is a newly emerging mathematical tool for dealing with uncertain problems. Parameter reduction abandons redundant parameters meanwhile holds the powerful ability to support decision making Ma et al. (2014) expressed four diverse parameter reduction approaches which are appropriate for the different scenarios. Optimal choice considered parameter reduction approach is not effective to support the additive parameters. The other three methods provide the support for the newly additive parameters but possess very low rate of success. And the four methods are computationally complicated. In this paper, we propose Pearson’s product moment coefficient based parameter reduction algorithm for an interval-valued fuzzy soft sets. By comparison with four algorithms, this approach not only is carried out before getting the scores, give attention to the newly additive parameters, and has much higher probability to find parameter reduction, but also is not more computationally complicated. Therefore, this algorithm is the most efficient to support extension and combination of multiple evaluation systems based on interval-valued fuzzy soft set in the down-to-earth applications environment. The superiority and effectiveness of the proposed approach is demonstrated by this means of a suitable practical application case of on-line reservation for accommodation and twenty synthetic generated datasets.

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
Fig. 2

Similar content being viewed by others

References

  1. Molodtsov D (1999) Soft set theory_First results. Comput Math Appl 37(4/5):19–31

    MathSciNet  MATH  Google Scholar 

  2. Han B (2016) Normal parameter reduction in soft set based on particle swarm optimization algorithm. Appl Math Model 40:10828–10834

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  6. Herawan T, Mat Deris M (2011) A Soft Set Approach for Association Rules Mining. Knowl-Based Syst 24(1):186–195

    MATH  Google Scholar 

  7. Qin H, Ma X, Herawan T, Zain JM (2012) DFIS: a novel data filling approach for an incomplete soft set. Int J Appl Math Comput Sci 22:817–828

    MathSciNet  MATH  Google Scholar 

  8. Qin H, Ma X, Zain JM, Herawan T (2012) A novel soft set approach for selecting clustering attribute. Knowl-Based Syst 36:139–145

    Google Scholar 

  9. 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 38:2141–2150

    MathSciNet  MATH  Google Scholar 

  10. Chen D, Tsang ECC, Yeung DS, Wang X (2005) The parameterization reduction of soft sets and its applications. Comput Math Appl 49(5–6):757–763

    MathSciNet  MATH  Google Scholar 

  11. 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  MATH  Google Scholar 

  12. Ma X, Sulaiman N, Qin H, Herawan T, Zain JM (2011) A new efficient Normal parameter ReductionAlgorithm of soft sets. Comput Math Appl 62:588–598

    MathSciNet  MATH  Google Scholar 

  13. Ma X, Qin H, Sulaiman N, Herawan T, Abawajy J (2014) The parameter reduction of the interval-valued fuzzy soft sets and its related algorithms. IEEE Trans Fuzzy Syst 22(1):57–71

    Google Scholar 

  14. Ma X, Qin H (2018) A Distance-Based Parameter Reduction Algorithm of Fuzzy Soft Sets. IEEE Access 6:10530–10539

    Google Scholar 

  15. Kong Z, Ai J, Wang L, Li P, Ma L, Lu F (2019) New Normal parameter reduction method in fuzzy soft set theory. IEEE Access 7:2986–2998

    Google Scholar 

  16. Han B, Li Y, Geng S (2017) 0–1 linear programming methods for optimal normal and pseudo parameter reductions of soft sets. Appl Soft Comput 54:467–484

    Google Scholar 

  17. Qin H, Ma X (2019) Data Analysis Approaches of Interval-Valued Fuzzy Soft Sets Under Incomplete Information. IEEE Access 7:3561–3571

    Google Scholar 

  18. Qin H, Ma X (2018) A Complete Model for Evaluation System Based on Interval-Valued Fuzzy Soft Set. IEEE Access 6:35012–35028

    Google Scholar 

  19. Yang X, Lin TY, Yang J, Dongjun YLA (2009) Combination of interval-valued fuzzy set and soft set. Comput Math Appl 58:521–527

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  21. Peng X, Harish G (2018) Algorithms for interval-valued fuzzy soft sets in emergency decision making based on WDBA and CODAS with new information measure. Comput Ind Eng 119:439–452

    Google Scholar 

  22. Peng X, 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 54:415–430

    Google Scholar 

  23. Ma X, Fei Q, Qin H, Zhou X, Li H (2019) New improved Normal parameter reduction method for fuzzy soft set. IEEE Access 7:154912–154921

    Google Scholar 

  24. 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(16):4808–4820

    MathSciNet  MATH  Google Scholar 

  25. Das S, Kar S (2015) Group decision making in medical system: an intuitionistic fuzzy soft set approach. Appl Soft Comput 24:196–211

    Google Scholar 

  26. Galton F (1886) Regression towards mediocrity in hereditary stature. J Anthropol Inst G B Irel 15:246–263

    Google Scholar 

  27. Pearson K (1895) Notes on regression and inheritance in the case oftwoparents. Proc R Soc Lond 58:240–242

    Google Scholar 

  28. Stigler SM (1989) Francis Galton's Account of the Invention of Correlation. Stat Sci 4(2):73–79

    MathSciNet  MATH  Google Scholar 

  29. Gorzalzany MB (1987) A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst 21:1–17

    MathSciNet  Google Scholar 

  30. Zhan J, Ali MI, Mehmood N (2017) On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods. Appl Soft Comput 56:446–457

    Google Scholar 

Download references

Acknowledgements

This work was supported by the National Science Foundation of China (No. 61662067, 61662068).

Author information

Authors and Affiliations

  1. College of Computer Science and Engineering, Northwest Normal University, Lanzhou, 730070, Gansu, China

    Xiuqin Ma & Hongwu Qin

Authors
  1. Xiuqin Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hongwu Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiuqin Ma.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ma, X., Qin, H. A new parameter reduction algorithm for interval-valued fuzzy soft sets based on Pearson’s product moment coefficient. Appl Intell 50, 3718–3730 (2020). https://doi.org/10.1007/s10489-020-01708-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-020-01708-1

Keywords

Search

Navigation