Mathematics in Computer Science

, Volume 7, Issue 3, pp 353–365 | Cite as

Intuitionistic Fuzzy Soft K-Algebras

  • Muhammad Akram
  • Bijan Davvaz
  • Feng Feng


Intuitionistic fuzzy sets and soft sets are two different soft computing models for representing vagueness and uncertainty. We apply these soft computing models in combination to study vagueness and uncertainty in K-algebras. We first introduce the notion of \({(\in, \in\vee q)}\)-intuitionistic fuzzy K-algebras and discuss some of their properties. Then we introduce intuitionistic fuzzy soft K-algebras and investigate some of their properties. Finally, we introduce \({(\in, \in \vee q)}\)-intuitionistic fuzzy soft K-algebras and present some of their related properties.


K-algebras \({(\in, \in \vee q)}\)-intuitionistic fuzzy K-algebra Intuitionistic fuzzy K-subalgebras \({(\in, \in \vee q)}\)-intuitionistic fuzzy soft K-algebra 

Mathematical Subject Classification (2000)

20N15 94D05 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abdullah S., Davvaz B., Aslam M.: (α, β)-intuitionistic fuzzy ideals of hemirings. Comput. Math. Appl. 62(8), 3077–3090 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Akram M., Davvaz B.: Generalized fuzzy ideals of K-algebras. J. Multivalued Soft Comput. 19, 475–491 (2012)MathSciNetGoogle Scholar
  3. 3.
    Akram M.: Bifuzzy ideals of K-algebras. WSEAS Trans. Math. 7(5), 313–322 (2008)MathSciNetGoogle Scholar
  4. 4.
    Akram M., Al-Shehrie N.O., Alghamdi R.S.: Fuzzy soft K-algebras. Utilitas Mathematica 90, 307–325 (2013)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Ali M.I., Feng F., Liu X.Y., Min W.K., Shabir M.: On some new operations in soft set theory. Comput. Math. Appl. 57, 1547–1553 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Atanassov, K.T.: Intuitionistic fuzzy sets. VII ITKR’s Session, Sofia, June 1983, Deposed in Central Sci-Techn. Library of Bulg. Acad. of Sci., 1697/84 (in Bulgarian)Google Scholar
  7. 7.
    Bhakat S.K., Das P.: \({(\in, \in \vee q)}\)-fuzzy subgroup. Fuzzy Sets Syst. 80, 359–368 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Coker D., Demirci M.: On intuitionistic fuzzy points. Notes IFS 1(2), 79–84 (1995)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Dar K.H., Akram M.: On a K-algebra built on a group. Southeast Asian Bull. Math. 29(1), 41–49 (2005)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Dar K.H., Akram M.: On K-homomorphisms of K-algebras. Int. Math. Forum 46, 2283–2293 (2007)MathSciNetGoogle Scholar
  11. 11.
    Feng F., Li C.X., Davvaz B., Irfan Ali M.: Soft sets combined with fuzzy sets and rough sets: a tentative approach. Soft Comput. 14, 899–911 (2010)CrossRefzbMATHGoogle Scholar
  12. 12.
    Feng F., Jun Y.B., Liu X.Y., Li L.F.: An adjustable approach to fuzzy soft set based decision making. J. Comput. Appl. Math. 234, 10–20 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Feng F., Liu X.Y., Leoreanu-Fotea V., Jun Y.B.: Soft sets and soft rough sets. Inf. Sci. 181, 1125–1137 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Maji P.K., Biswas R., Roy R.: Soft set theory. Comput. Math. Appl. 45, 555–562 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Maji P.K., Biswas R., Roy A.R.: Intuitionistic fuzzy soft sets. J. Fuzzy Math. 9(3), 677–692 (2001)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Molodtsov D.: Soft set theory first results. Comput. Math. Appl. 37, 19–31 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Pu P.M., Liu Y.M.: Fuzzy topology, I. Neighborhood structure of a fuzzy point and Moore-Smith convergence. J. Math. Anal. Appl. 76(2), 571–599 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Yang C.-F.: Fuzzy soft semigroups and fuzzy soft ideals. Comput. Math. Appl. 61, 255–561 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Zadeh L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Zhou J., Li Y., Yin Y.: Intuitionistic fuzzy soft semigroups. Mathematica Aeterna 1, 173–183 (2011)MathSciNetGoogle Scholar
  21. 21.
    Yin, Y., Zhan, J.: The characterizations of hemirings in terms of fuzzy soft h-ideals. Neural Comput. Appl. doi: 10.1007/s00521-011-0591-9
  22. 22.
    Zhan J., Jun Y.B.: Soft BL-algebras based on fuzzy sets. Comput. Math. Appl. 59, 2037–2046 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Dudek W.A.: . Sci. Bull. Series A Appl. Math. Phys. Politeh. Univ. Bucharest 74, 41–56 (2012)MathSciNetzbMATHGoogle Scholar
  24. 24.
    Yin Y.Q., Jun Y.B., Zhan J.M.: Vague soft hemirings. Comput. Math. Appl. 62, 199–213 (2011)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Punjab University College of Information TechnologyUniversity of the PunjabLahorePakistan
  2. 2.Department of MathematicsYazd UniversityYazdIran
  3. 3.Department of Applied MathematicsXi’an University of Posts and TelecommunicationsXi’anChina

Personalised recommendations