Skip to main content
SpringerLink
Log in

Decision Analysis Methods Combining Quantitative Logic and Fuzzy Soft Sets

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

In this paper we propose a new decision analysis method combining quantitative logic and fuzzy soft set theory. Firstly, we transform a fuzzy information system into a fuzzy soft set, and then establish a formal language based on the fuzzy soft set, in which the parameters of fuzzy soft set are regarded as atomic formulas, some atomic formulas are connected by the logical connectives and then a logical formula is formed, and a implicative type of formula is interpreted as a soft decision rule (SDR). Secondly, various types of measures to evaluate the SDR are introduced and then the soft metric between two logical formulas is established. Thirdly, we apply the soft metric to the soft decision analysis, a SDR extraction algorithm for fuzzy decision information system and a corresponding recommendation algorithm are proposed. Finally, some attribute analysis examples, including the example as shown in rough sets and the practical credit card application example, are given to illustrate the newly proposed method and related concepts.

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. Stewart, T.J.: A critical survey on the status of multiple criteria decision making theory and practice. Omega 20, 569–586 (1992)

    Article  Google Scholar 

  2. Fan, Z.P., Feng, B.: A multiple attributes decision-making method using individual and collaborative attribute data in a fuzzy environment. Inform. Sci. 179, 3603–3618 (2009)

    Article  Google Scholar 

  3. Yue, Z.L.: An extended TOPSIS for determining weights of decision-makers with interval numbers. Knowl. Based Syst. 24, 146–153 (2011)

    Article  Google Scholar 

  4. Torra, V., Narukawa, Y.: On hesitant fuzzy sets and decisions. In: IEEE international conference on fuzzy systems, pp. 1378–1382 (2009)

  5. Akram, M., Adeel, A., Alcantud, J.C.R.: Group decision-making methods based on hesitant N-soft sets. Expert Syst. Appl. 115, 95–105 (2019)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  7. Jiang, Y., Tang, Y., Chen, Q., Wang, J.: Extending soft sets with description logics. Comput. Math. Appl. 59, 2087–2096 (2010)

    Article  MathSciNet  Google Scholar 

  8. Mushrif, M.M., Sengupta, S., Ray, A.K.: Texture classification using a novel, soft set theory based classification algorithm. Lecture Notes Comput. Sci. 3851, 246–254 (2006)

    Article  Google Scholar 

  9. Maji, P.K., Roy, A.R.: An application of soft sets in a decision making problem. Comput. Math. Appl. 44, 1077–1083 (2002)

    Article  MathSciNet  Google Scholar 

  10. Roy, A.R., Maji, P.K.: A fuzzy soft set theoretic approach to decision making problems. J. Comput. Appl. Math. 203(3), 412–418 (2007)

    Article  Google Scholar 

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

    Article  Google Scholar 

  12. Zhan, J.M., Liu, Q., Herawan, T.: A novel soft rough set: soft rough hemirings and corresponding multicriteria group decision making. Appl. Soft Comput. 54, 393–402 (2017)

    Article  Google Scholar 

  13. Ma, X.L., Liu, Q., Zhan, J.M.: A survey of decision making methods based on certain hybrid soft set models. Artif. Intell. Rev. 47, 507–530 (2017)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  15. Geng, S.L., Li, Y.M., Liu, Z.: An approach to association rules mining using inclusion degree of soft sets. Acta Electronica Sinica 41(4), 804–809 (2013). (in Chinese)

    Google Scholar 

  16. Jiang, Y.C., Liu, H., Tang, Y., Chen, Q.: Semantic decision making using ontology-based soft sets. Math. Comput. Model. 53(5), 1140–1149 (2011)

    Article  MathSciNet  Google Scholar 

  17. Wang, G.J., Zhou, H.J.: Quantitative logic. Inform. Sci. 179(3), 226–247 (2009)

    Article  MathSciNet  Google Scholar 

  18. Hui, X.J., Wang, G.J.: Randomization of classical inference patterns and its application. Sci. China F 50, 867–877 (2007)

    MathSciNet  MATH  Google Scholar 

  19. Zhou, H.J.: Theory of Borel probability truth degree of propositions in Lukasiewicz propositional logics and a limit theorem. J. Softw. 23(9), 2535–2547 (2012)

    Article  Google Scholar 

  20. Wu, X., Zhang, J.L.: Truth theory of proposition logic under random fuzzy environment. Patt. Recogn. Artif. Intell. 30(4), 289–301 (2017)

    Google Scholar 

  21. Zhang, J.L., Chen, X.G., Zhao, X.D.: Theory of probability semantics of classical propositional logic and its application. Chin. J. Comput. 37(8), 1775–1785 (2014)

    Google Scholar 

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

    Article  Google Scholar 

  23. Zhang, W.X., Liang, Y., Wu, W.Z.: Information systems and knowledge discoveries. Science Press, Beijing (2003)

    Google Scholar 

  24. Zhang, J.L., Liu, X.L.: Fuzzy belief measure in random fuzzy information systems and its application to knowledge reduction. Neural Comput. Appl. 22, 1419–1431 (2013)

    Article  Google Scholar 

  25. Klement, E.P., Lowen, R., Schwyha, W.: Fuzzy probability measures. Fuzzy Sets Syst. 1, 21–30 (1981)

    Article  MathSciNet  Google Scholar 

  26. Xu, H.L., Wu, X., Li, X.D., et al.: The comparison of internet recommendation systems. J. Softw. 20(2), 350–362 (2009)

    Article  Google Scholar 

  27. Li, C., Liang, C.Y., Ma, L.: A collaborative filtering recommendation algorithm based on domain nearest neighbor. J. Comput. Res. Dev. 45(9), 1532–1538 (2008)

    Google Scholar 

  28. Kim, J., Cho, Y., Kim, W., et al.: A personalized recommendation procedure for internet shopping support. Electron. Commer. Res. Appl. 1, 301–313 (2002)

    Article  Google Scholar 

  29. Zadeh, L.A.: Fuzzy sets. Inform. Control 8, 338–353 (1965)

    Article  Google Scholar 

  30. Pawlak, Z., Skowron, A.: Rudiments of rough sets. Inform. Sci. 177, 3–27 (2007)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mathematics and Finance, Xiangnan University, Chenzhou, 426000, China

    Jialu Zhang & Xia Wu

  2. College of Software and Communication Engineering, Xiangnan University, Chenzhou, 423000, China

    Ruhua Lu

Authors
  1. Jialu Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xia Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ruhua Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xia Wu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, J., Wu, X. & Lu, R. Decision Analysis Methods Combining Quantitative Logic and Fuzzy Soft Sets. Int. J. Fuzzy Syst. 22, 1801–1814 (2020). https://doi.org/10.1007/s40815-020-00899-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-020-00899-6

Keywords

Search

Navigation