The Journal of Analysis

, Volume 27, Issue 1, pp 151–160 | Cite as

On quotient BF-algebras via interval-valued intuitionistic fuzzy ideals

  • D. RameshEmail author
  • B. Satyanarayana
  • N. Srimannarayana
Original Research Paper


The present paper gives a new construction of a quotient BF-algebra \( {\raise0.5ex\hbox{$\scriptstyle X$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle I$}} \) by an interval-valued intuitionistic fuzzy ideal I in BF-algebra X, we show that if I is a interval-valued intuitionistic fuzzy ideal of BF-algebra X, then \( {\raise0.5ex\hbox{$\scriptstyle X$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle I$}} \) is a BF-algebra if and only if I is an interval-valued intuitionistic fuzzy ideal of BF-algebra X and investigate some of its properties.


BF-algebras Intuitionistic fuzzy set Interval-valued intuitionistic fuzzy ideals 

Mathematics Subject Classifications

06F35 03E72 46S40 


Compliance with ethical standards

Conflict of interest

All the authors declare that they have no conflict of interest.


  1. 1.
    Soeid, Borumand, and M.A. Rezvani. 2009. On fuzzy BF-algebras. International Mathematical Forum 4: 13–25.MathSciNetzbMATHGoogle Scholar
  2. 2.
    Liu, Y.L., and J. Meng. 2002. Construction of quotient BCI (BCK)-algebras via a fuzzy ideal. Journal of Applied Mathematics and Computing 10 (1–2): 51–62.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Satyanarayana, B., D. Ramesh, M.K. Vijaya Kumar, and R. Durga Prasad. 2010. On fuzzy ideals in BF-algebras. International Journal of Science Engineering Applications 4: 263–274.MathSciNetGoogle Scholar
  4. 4.
    Satyanarayana, B., M.V. Kumar, D. Ramesh, and R. Durga Prasad. 2012. Interval-valued intuitionistic fuzzy BF-subalgebras. Acta Cienceia Indica XXXVIII M 4: 637–644.Google Scholar
  5. 5.
    Hema, Ramesh P., P.H. Sundari, and B. Satyanarayana. 2016. On Quotient BF-algebra via interval-valued fuzzy ideals. IJFMA 10: 169–174.Google Scholar
  6. 6.
    Walendziak, A. 2007. On BF-algebras. Mathematica Slovaca 57 (2): 11.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Zadeh, L.A. 1965. Fuzzy sets. Information, Control 8: 338–353.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Zadeh, L.A. 1975. The concept of a linguistic variable and its application to approximate reasoning. Information Sciences 8: 199–249.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Forum D'Analystes, Chennai 2018

Authors and Affiliations

  1. 1.Department of MathematicsK.L.E.FGunturIndia
  2. 2.Department of MathematicsAcharya Nagarjuna UniversityGunturIndia

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