L-Fuzzy Filters of a Poset

Berhanu Assaye Alaba, Mihret Alamneh, Derso Abeje

Abstract


Many generalizations of ideals and filters of a lattice to an arbitrary poset have been studied by different scholars. The authors of this paper introduced several generalizations of L-fuzzy ideal of a lattice to an arbitrary poset in [1]. In this paper, we introduce several L-fuzzy filters of a poset which generalize the L-fuzzy filter of a lattice and give several characterizations of them.

Keywords


Poset; Filter; L-fuzzy closed Filter; L-fuzzy Frink Filter; L-fuzzy V-Filter; L-fuzzy M-Filter; L-fuzzy Semi-Filter; L-Fuzzy Filter; l-L-fuzzy filter

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References


B. Alaba, M. Taye, and D. Engidaw, “L-fuzzy ideals of a poset,” Ann. Fuzzy Math. Inform., vol. 16, pp. 285–299, 2018.

G. Birkhoff, Lattice theory. American Mathematical Soc., 1940, vol. 25.

M. Stone, “The theory of representation for boolean algebras,” Transactions of the American Mathematical Society, vol. 40, no. 1, pp. 37–111, 1936.

O. Frink, “Ideals in partially ordered sets,” The American Mathematical Monthly, vol. 61, no. 4, pp. 223–234, 1954.

P. Venkatanarasimhan, “Pseudo-complements in posets,” Proceedings of the American Mathematical Society, vol. 28, no. 1, pp. 9–17, 1971.

P. Venkatanarasimhan, “Semi-ideals in posets,” Mathematische Annalen, vol. 185, no. 4, pp. 338–348, 1970.

R. Halas, “Annihilators and ideals in ordered sets,” Czechoslovak Mathematical Journal, vol. 45, no. 1, pp. 127–134, 1995.

N. Ajmal and K. Thomas, “Fuzzy lattices,” Information sciences, vol. 79, no. 3-4, pp. 271–291, 1994.

B. Koguep, C. Nkuimi, and C. Lele, “On fuzzy prime ideals of lattice,” SJPAM, vol. 3, pp. 1–11, 2008.

T. Rao, C. Rao, D. Solomon, and D. Abeje, “Fuzzy ideals and filters of lattices,” Asian Journal of Current Engineering and Maths, vol. 2, no. 4, 2013.

U. Swamy and D. Raju, “Fuzzy ideals and congruences of lattices,” Fuzzy sets and systems, vol. 95, no. 2, pp. 249–253, 1998.

Y. Bo and W. Wangming, “Fuzzy ideals on a distributive lattice,” Fuzzy sets and systems, vol. 35, no. 2, pp. 231–240, 1990.

B. Davey and H. Priestley, Introduction to lattices and order. Cambridge university press, 2002.

G. Gratzer, General lattice theory. Springer Science & Business Media, 2002.

R. Halas and J. Rachunek, “Polars and prime ideals in ordered sets,” Discuss. Math., Algebra Stoch. Methods, vol. 15, pp. 43–59, 1995.

J. Goguen, “L-fuzzy sets,” Journal of mathematical analysis and applications, vol. 18, no. 1, pp. 145–174, 1967.

L. Zadeh, “Fuzzy sets,” Information and control, vol. 8, no. 3, pp. 338–353, 1965.

J. Mordeson and D. Malik, Fuzzy commutative algebra. World scientific, 1998.




DOI: http://dx.doi.org/10.12962/j24775401.v5i1.3779

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International Journal of Computing Science and Applied Mathematics by Department Mathematics ITS is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at http://iptek.its.ac.id/index.php/ijcsam.