Note on fuzzy soft sets and fuzzy soft lattices

  • Noor Rehman
  • Abbas Ali
  • Choonkil ParkEmail author
Original Paper


In this note, we point out that several assertions (Proposition 7, Lemmas 20, 21 and Theorems 7, 15) in [Y. Shao and K. Qin, Fuzzy soft sets and fuzzy soft lattices, Int. J. Comput. Intell. Sys. 5 (2012), 1135–1147] are not true in general. Appropriate counterexamples are given. Further their modified versions are presented.


Soft set Fuzzy soft set Lattice Fuzzy soft latice 

Mathematics Subject Classification

Primary 06D72 03E72 94D05 



C. Park was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (NRF-2017R1D1A1B04032937).


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    Ali, M.I., Feng, F., Liu, X., Min, W.K., Shabir, M.: On some new operations in soft set theory. Comput. Math. Appl. 57, 1547–1553 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
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    Qin, K., Hong, Z.: On soft equality. J. Comput. Appl. Math. 234, 1347–1355 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
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    Shao, Y., Qin, K.: Fuzzy soft sets and fuzzy soft lattices. Int. J. Comput. Int. Sys. 5, 1135–1147 (2012)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Italia S.r.l. 2017

Authors and Affiliations

  1. 1.Departmant of Mathematics and StatisticsRiphah International UniversityIslamabadPakistan
  2. 2.Department of Mathematics, Research Institute of Natural SciencesHanyang UniversitySeoulRepublic of Korea

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