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Entropy for Multiaspect Fuzzy Soft Sets and Its Application in Group Decision Making

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Proceedings of the International Conference on Data Engineering 2015 (DaEng-2015)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 520))

Abstract

In this paper, we introduce an axiomatic definition of entropy for multiaspect fuzzy soft sets (MAFSS). An entropy measure based on the definition is established and the properties are investigated. The entropy is then used to derive an entropy weight formulation. The entropy weight can be applied in aggregating a collection of MAFSSs which are particularly useful in the context of group decision making under MAFSS environment.

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References

  1. Luca, A.D., Termini, S.: A definition of non-probabilistic entropy in the setting of fuzzy theory. Inf. Control 20, 301–312 (1972)

    Article  Google Scholar 

  2. Liu, X.: Entropy, distance measure and similarity measure of fuzzy sets and their relations. Fuzzy Sets Syst. 52, 305–318 (1992)

    Article  MathSciNet  Google Scholar 

  3. Zhang, H., Zhang, W., Mei, C.: Entropy of interval-valued fuzzy sets based on distance and its relationship with similarity measure. Knowl. Based Syst. 22(6), 449–454 (2009)

    Article  Google Scholar 

  4. Liu, Z., Qin, K., Pei, Z.: Similarity measure and entropy of fuzzy soft sets. Sci. World J. 2014, Article ID161607, 10 p (2014)

    Google Scholar 

  5. Farhadinia, B.: A theoretical development on the entropy of interval-valued fuzzy sets based on the intuitionistic distance and its relationship with similarity measure. Knowl. Based Syst. 39, 79–84 (2013)

    Article  Google Scholar 

  6. Wu, J.Z., Zhang, Q.: Multicriteria decision making method based on intuitionistic fuzzy weighted entropy. Expert Syst. Appl. 38, 916–922 (2011)

    Article  Google Scholar 

  7. Khaleie, S., Fasanghari, M.: An intuitionistic fuzzy group decision making method using entropy and association coefficient. Soft. Comput. 16, 1197–1211 (2012)

    Article  Google Scholar 

  8. Zhang, Q.S., Jiang, S.Y.: A note on entropy measures for vague sets and its applications. Inf. Sci. 178, 4184–4191 (2008)

    Article  MathSciNet  Google Scholar 

  9. Jiang, Y., Tang, Y., Liu, H., Chen, Z.: Entropy on intuitionistic fuzzy soft sets and on interval-valued fuzzy soft sets. Inf. Sci. 240, 95–114 (2013)

    Article  MathSciNet  Google Scholar 

  10. Jaganathan, R., Kuppuchamy, P.: A threshold fuzzy entropy based feature selection for medical database classification. Comput. Biol. Med. 43, 2222–2229 (2013)

    Article  Google Scholar 

  11. Shie, J.D., Chen, S.M.: Feature subset selection based on fuzzy entropy measures for handling classification problems. Appl. Intell. 28, 69–82 (2008)

    Article  Google Scholar 

  12. Chen, T.Y., Li, C.H.: Determining objective weights with intuitionistic fuzzy entropy measures: a comparative analysis. Inf. Sci. 180, 4207–4222 (2010)

    Article  Google Scholar 

  13. Xia, M., Xu, Z.: Entropy/cross entropy-based group decision making under intuitionistic fuzzy environment. Inf. Fusion 13, 31–47 (2012)

    Article  Google Scholar 

  14. Zou, Z.H., Yun, Y., Sun, J.N.: Entropy method for determination of weights of evaluating indicators in fuzzy synthetic evaluation for water quality assessment. J. Environ. Sci. 18(5), 1020–1023 (2006)

    Article  Google Scholar 

  15. Juang, C.H., Huang, X.H.: Aggregating expert opinion by fuzzy entropy method. Civil Eng. Syst. 9(2), 89–104 (1992)

    Article  Google Scholar 

  16. Liang, X., Wei, C.: An Atanassov’s intuitionistic fuzzy multiattribute group decision making method based on entropy and similarity measure. Int. J. Mach. Learn. Cybern. (2013) https://doi.org/10.1007/s13042-013-0178-0

    Article  Google Scholar 

  17. Sulaiman, N.H., Mohamad, D.: Multiaspect fuzzy soft sets and their properties. Appl. Math. Sci. 6(115), 5709–5718 (2012)

    MathSciNet  MATH  Google Scholar 

  18. Sulaiman, N.H., Mohamad, D.: Mapping on multiaspect fuzzy soft classes. In: AIP Conference Proceedings of the 3rd International Conference on Mathematical Sciences, vol. 1602, pp. 716–722 (2014)

    Google Scholar 

  19. Maji, P.K., Biswas, R., Roy, A.R.: Fuzzy soft sets. J. Fuzzy Math. 9(3), 589–602 (2001)

    MathSciNet  MATH  Google Scholar 

  20. Sulaiman, N.H., Mohamad, D.: Multiaspect soft sets. Adv. Fuzzy Syst. 2013, Article ID 680486, 11p (2013)

    Google Scholar 

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

    Article  Google Scholar 

  22. Sulaiman, N.H., Mohamad, D.: Aggregation operations for Multiaspect Fuzzy Soft Sets. Presented in the 22nd National Symposium on Mathematical Science, Shah Alam, Malaysia, 24–26 Nov 2015

    Google Scholar 

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Acknowledgements

The authors would like to thank Universiti Teknologi MARA Malaysia and the Ministry of Higher Education, Malaysia for the financial support received.

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Correspondence to Daud Mohamad .

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Sulaiman, N.H., Mohamad, D. (2019). Entropy for Multiaspect Fuzzy Soft Sets and Its Application in Group Decision Making. In: Abawajy, J., Othman, M., Ghazali, R., Deris, M., Mahdin, H., Herawan, T. (eds) Proceedings of the International Conference on Data Engineering 2015 (DaEng-2015) . Lecture Notes in Electrical Engineering, vol 520. Springer, Singapore. https://doi.org/10.1007/978-981-13-1799-6_30

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