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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


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Volume 63, Issue 5

Issues

Fuzzy filters of BE-algebras

Grzegorz Dymek
  • Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin, Konstantynów 1H, PL-20-708, Lublin, Poland
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/ Andrzej Walendziak
  • Institute of Mathematics and Physics, Siedlce University of Natural Sciences and Humanities, 3 Maja 54, PL-08-110, Siedlce, Poland
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Published Online: 2013-11-01 | DOI: https://doi.org/10.2478/s12175-013-0145-y

Abstract

Characterizations of fuzzy filters in a BE-algebra are established. Conditions for a fuzzy set to be a fuzzy filter are given. For a fuzzy set µ the least fuzzy filter containing µ is constructed. The homomorphic properties of fuzzy filters of a BE-algebra are provided. Finally, characterizations of Noetherian BE-algebras and Artinian BE-algebras via fuzzy filters are obtained.

MSC: Primary 03G25; Secondary 06F35

Keywords: BE-algebra; fuzzy filter; Noetherian (Artinian) BE-algebra

  • [1] AHN, S. S.— SO, K. S.: On ideals and upper sets in BE-algebras, Sci. Math. Jpn. e-2010, 351–357. Google Scholar

  • [2] HU Q. P.— LI, X.: On BCH-algebras, Math. Seminar Notes 11 (1983), 313–320. Google Scholar

  • [3] IMAI, Y.— ISÉKI, K.: On axiom systems of propositional calculi XIV, Proc. Japan Acad. Ser. A Math. Sci. 42 (1966), 19–22. http://dx.doi.org/10.3792/pja/1195522169CrossrefGoogle Scholar

  • [4] ISÉKI, K.: An algebra related with a propositional calculus, Proc. Japan Acad. Ser. A Math. Sci. 42 (1966), 26–29. http://dx.doi.org/10.3792/pja/1195522171CrossrefGoogle Scholar

  • [5] JUN, Y. B.— ROH, E. H.— KIM, H. S.: On BH-algebras, Sci. Mathematicae 1 (1998), 347–354. Google Scholar

  • [6] KIM, H. S.— KIM, Y. H.: On BE-algebras, Sci. Math. Jpn. 66 (2007), 113–116. Google Scholar

  • [7] KIM, H. S.— LEE, K. J.: Extended upper sets in BE-algebras, Bull Malays. Math. Sci. Soc. (2) 34 (2011), 511–520. Google Scholar

  • [8] KOMORI, Y.: The variety generated by BCC-algebras is finitelly based, Rep. Fac. Sci. Shizuoka Univ. 17 (1983), 13–16. Google Scholar

  • [9] MENG, B. L.: On filters in BE-algebras, Sci. Math. Jpn. e-2010, 105–111. Google Scholar

  • [10] NEGGERS, J.— KIM, H. S.: On d-algebras, Math. Slovaca 40 (1999), 19–26. Google Scholar

  • [11] SONG, S. Z.— JUN, Y. B.— LEE, K. J.: Fuzzy ideals in BE-algebras, Bull Malays. Math. Sci. Soc. (2) 33 (2010), 147–153. Google Scholar

About the article

Published Online: 2013-11-01

Published in Print: 2013-10-01


Citation Information: Mathematica Slovaca, Volume 63, Issue 5, Pages 935–946, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.2478/s12175-013-0145-y.

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© 2013 Mathematical Institute, Slovak Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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