Afrika Matematika

, Volume 25, Issue 4, pp 1197–1210

Anti fuzzy filters of \(CI\)-algebras

  • Rajab Ali Borzooei
  • Arsham Borumand Saeid
  • Akbar Rezaei
  • Reza Ameri
Article

DOI: 10.1007/s13370-013-0183-1

Cite this article as:
Borzooei, R.A., Borumand Saeid, A., Rezaei, A. et al. Afr. Mat. (2014) 25: 1197. doi:10.1007/s13370-013-0183-1
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Abstract

In this paper, we introduce the notion of anti fuzzy filter and study the \(\mathcal{N }\)-subalgebra(filter) of \(CI\)-algebra \(X\). We prove that every anti fuzzy filter of \(BE\)-algebra is an anti fuzzy subalgebra, but it is not valid in \(CI\)-algebra. Finally, the notion of fuzzy translations and fuzzy extension of anti fuzzy filter in \(CI\)-algebras are introduced. We show that every anti fuzzy filter can be as an anti fuzzy extension, but converse may not be true in general.

Keywords

\(CI\)-algebra \(\mathcal{N }\)-subalgebra(filter) Anti fuzzy subalgebra(filter) 

Mathematics Subject Classification (2010)

06F35 03G25 03E72 

Copyright information

© African Mathematical Union and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Rajab Ali Borzooei
    • 1
  • Arsham Borumand Saeid
    • 2
  • Akbar Rezaei
    • 3
  • Reza Ameri
    • 4
  1. 1.Department of MathematicsShahid Beheshti University of TehranTehranIran
  2. 2.Department of MathematicsShahid Bahonar University of KermanKermanIran
  3. 3.Department of MathematicsPayame Noor UniversityTehranIran
  4. 4.Department of MathematicsTehran UniversityTehranIran

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