The Prominentness of Fuzzy GE-Filters in GE-Algebras

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DOI: https://doi.org/10.28924/2291-8639-21-2023-26
Published: Mar 17, 2023
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Sun Shin Ahn, Rajab Ali Borzooei, Young Bae Jun, The Prominentness of Fuzzy GE-Filters in GE-Algebras, Int. J. Anal. Appl., 21 (2023), 26.

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Sun Shin Ahn, Rajab Ali Borzooei, Young Bae Jun

Abstract

Based on the concept of fuzzy points, the notion of a prominent fuzzy GE-filter is defined, and the various properties involved are investigated. The relationship between a fuzzy GE-filter and a prominent fuzzy GE-filter is discussed, and the characterization of a prominent fuzzy GE-filter is considered. The conditions under which a fuzzy GE-filter can be a prominent fuzzy GE-filter are explored, and conditions for the trivial fuzzy GE-filter to be a prominent fuzzy GE-filter are provided. The conditions under which the ∈t-set and Qt-set can be prominent GE-filters are explored. Finally, the extension property for the prominent fuzzy GE-filter is discussed.

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References

  1. R.K. Bandaru, T.G. Alemayehu, Y.B. Jun, Fuzzy GE-Filters of GE-Algebras, J. Algebra Related Topics. (submitted).
  2. R. Bandaru, A.B. Saeid, Y.B. Jun, On GE-Algebras, Bull. Sect. Logic. 50 (2020), 81–96. https://doi.org/10.18778/0138-0680.2020.20.
  3. R.K. Bandaru, M.A. Öztürk, Y.B. Jun, Bordered GE-algebras, J. Algebraic Syst. In Press.
  4. S. Celani, A Note on Homomorphisms of Hilbert Algebras, Int. J. Math. Math. Sci. 29 (2002), 55–61. https://doi.org/10.1155/s0161171202011134.
  5. I. Chajda, R. Halas, Y.B. Jun, Annihilators and Deductive Systems in Commutative Hilbert Algebras, Comment. Math. Univ. Carolin. 43 (2002), 407–417. http://dml.cz/dmlcz/119331.
  6. A. Diego, Sur les Algèbres de Hilbert, Collection de Logique Mathématique, Edition Hermann, Série A, XXI, (1966).
  7. S.M. Hong, Y.B. Jun, On Deductive Systems of Hilbert Algebras, Commun. Korean Math. Soc. 11 (1996), 595–600.
  8. Y.B. Jun, K.H. Kim, H-Filters of Hilbert Algebras, Sci. Math. Japon. e-2005 (2005), 231–236.
  9. H.S. Kim, Y.H. Kim, On BE-Algebras, Sci. Math. Japon. e-2006 (2006), 1299–1302.
  10. M.A. Öztürk, J.G. Lee, R. Bandaru, Y.B. Jun, Strong GE-Filters and GE-Ideals of Bordered GE-Algebras, J. Math. 2021 (2021), 5520023. https://doi.org/10.1155/2021/5520023.
  11. P.M. Pu, Y.M. Liu, Fuzzy Topology. I. Neighborhood Structure of a Fuzzy Point and Moore-Smith Convergence, J. Math. Anal. Appl. 76 (1980), 571–599. https://doi.org/10.1016/0022-247x(80)90048-7.
  12. A. Rezaei, R. Bandaru, A.B. Saeid, Y.B. Jun, Prominent GE-Filters and GE-Morphisms in GE-Algebras, Afr. Mat. 32 (2021), 1121–1136. https://doi.org/10.1007/s13370-021-00886-6.
  13. A. Rezaei, A. Borumand Saeid, R.A. Borzooei, Relation Between Hilbert Algebras and BE-Algebras, Appl. Appl. Math.: Int. J. 8 (2013), 573–584.
  14. S.Z. Song, R. Bandaru, Y.B. Jun, Imploring GE-Filters of GE-Algebras, J. Math. 2021 (2021), 1–7. https://doi.org/10.1155/2021/6651531.