Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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CO-FUZZY ANNIHILATOR FILTERS IN DISTRIBUTIVE LATTICES

  • Received : 2020.07.26
  • Accepted : 2020.10.29
  • Published : 2021.05.30
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Abstract

In this paper, we introduce the concept of relative co-fuzzy annihilator filters in distributive lattices. We give a set of equivalent conditions for a co-fuzzy annihilator to be a fuzzy filter and we characterize distributive lattices with the help of co-fuzzy annihilator filters. Furthermore, using the concept of relative co-fuzzy annihilators, we prove that the class of fuzzy filters of distributive lattices forms a Heyting algebra. We also study co-fuzzy annihilator filters. It is proved that the set of all co-fuzzy annihilator filters forms a complete Boolean algebra.

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References

  1. B.A. Alaba and W.Z. Norahun, Fuzzy annihilator ideals in distributive lattices, Ann. Fuzzy Math. Inform. 16 (2018), 191-200. https://doi.org/10.30948/afmi.2018.16.2.191
  2. B.A. Alaba and W.Z. Norahun, α-fuzzy ideals and space of prime α-fuzzy ideals in distributive lattices, Ann. Fuzzy Math. Inform. 17 (2019), 147-163. https://doi.org/10.30948/AFMI.2019.17.2.147
  3. B.A. Alaba and W.Z. Norahun, σ-fuzzy ideals of distributive p-algebras, Ann. Fuzzy Math. Inform. 17 (2019), 289-301. https://doi.org/10.30948/afmi.2019.17.3.289
  4. B.A. Alaba and W.Z. Norahun, Fuzzy ideals and fuzzy filters of pseudo-complemented semilattices, Advances in Fuzzy Systems 2019 (2019). 1-13.
  5. B.A. Alaba and G.M. Addis, L-Fuzzy prime ideals in universal algebras, Advances in Fuzzy Systems 2019 (2019). 1-7.
  6. B.A. Alaba and G.M. Addis, L-Fuzzy ideals in universal algebras, Ann. Fuzzy Math. Inform. 17 (2019), 31-39. https://doi.org/10.30948/afmi.2019.17.1.31
  7. B.A. Alaba and W.Z. Norahun, δ-fuzzy ideals in pseudo-complemented distributive lattices, J. Appl. Math. and Informatics 37 (2019), 383-397. https://doi.org/10.14317/jami.2019.383
  8. B.A. Alaba, M.A. Taye and W.Z. Norahun, d-fuzzy ideals in distributive lattices, Ann. Fuzzy Math. Inform. 18 (2019), 233-243. https://doi.org/10.30948/afmi.2019.18.3.233
  9. V. Amjid, F. Yousafzai and K. Hila, A Study of Ordered Ag-Groupoids in terms of Semi-lattices via Smallest (Fuzzy) Ideals, Advances in Fuzzy Systems 2018 (2018), 1-9.
  10. G. Birkhoff, Lattice theory, Colloquium Publication 25, Amer. Math. Soc., New York, 1948.
  11. O. Frink, Pseudo-complements in semi-lattices, Duke Math. J. 29 (1962), 505-514. https://doi.org/10.1215/S0012-7094-62-02951-4
  12. W.J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems 8 (1982), 133-139. https://doi.org/10.1016/0165-0114(82)90003-3
  13. M. Manderker, Relative annihilators in lattices, Duke Math. J. 37 (1970), 377-386. https://doi.org/10.1215/S0012-7094-70-03748-8
  14. N. Mordeson, K.R. Bhuntani and A. Rosenfeld, Fuzzy group theory, Springer, 2005.
  15. M.S. Rao and A.E. Badawy, µ-filters of distributive lattices, Southeast Asian Bulletin of Mathematics 48 (2016), 251-264.
  16. A. Rosenfeld, Fuzzy subgroups, J. Math. Anal. Appl. 35 (1971), 512-517. https://doi.org/10.1016/0022-247X(71)90199-5
  17. H.K. Saikia and M.C. Kalita, On annihilator of fuzzy subsets of modules, International Journal of Algebra 3 (2009), 483-488.
  18. T.P. Speed, A note on commutative semigroups, J. Austral. Math. Soc. 8 (1968), 731-736. https://doi.org/10.1017/S1446788700006558
  19. T.P. Speed, Some remarks on a class of distributive lattices, Jour. Aust. Math. Soc. 9 (1969), 289-296. https://doi.org/10.1017/S1446788700007205
  20. U.M. Swamy and D.V. Raju, Fuzzy ideals and congruences of lattices, Fuzzy Sets and Systems 95 (1998), 249-253. https://doi.org/10.1016/S0165-0114(96)00310-7
  21. B. Yuan and W. Wu, Fuzzy ideals on a distributive lattice, Fuzzy Sets and Systems 35 (1990), 231-240. https://doi.org/10.1016/0165-0114(90)90196-D
  22. L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X