Annals of Fuzzy Mathematics and Informatics

The Natural Science Institute Wonkwang University (원광대학교 기초자연과학연구소)
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L-fuzzy ideals of a poset

  • Received : 2018.06.20
  • Accepted : 2018.07.23
  • Published : 2018.12.25
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Abstract

Many generalizations of ideals of a lattice to an arbitrary poset have been studied by different scholars. In this paper, we introduce several L-fuzzy ideals of a poset which generalize the notion of an L-fuzzy ideal of a lattice and give several characterizations of them.

Keywords

References

  1. N. Ajmal and K. V. Thomas, Fuzzy lattices, Inform. Sci. 79 (1994) 271-291. https://doi.org/10.1016/0020-0255(94)90124-4
  2. G. Birkhoff, Lattice Theory. Amer. Math. Soc. Colloq. Publ. XXV, Revised Edition, Providence 1961.
  3. B. A. Davey and H. A. Priestley, Introduction to Lattices and Order, Cambridge Univ. Press, Cambridge 1990.
  4. M. Erne, Verallgemeinerungen der Verbandstheorie II: m-Ideale in halbgeordneten Mengen und Hullenraumen, Habilitationsschrift, University of Hannover 1979.
  5. M. Erne and Vinayak Joshi, Ideals in atomic posets, Discrete Mathematics 338 (2015) 954-971. https://doi.org/10.1016/j.disc.2015.01.001
  6. O. Frink, Ideals in partially ordered sets, Amer. Math. Monthly 61 (1954) 223-234. https://doi.org/10.1080/00029890.1954.11988449
  7. J. A. Goguen, L-fuzzy sets, J. Math. Anal. Appl. 18 (1967) 145-174. https://doi.org/10.1016/0022-247X(67)90189-8
  8. G. Gratzer, General Lattice Theory, Academic Press, New York 1978.
  9. R. Halas, Annihilators and ideals in ordered sets, Czechoslovak Math. J. 45 (120) (1995) 127-134.
  10. R. Halas, Decomposition of directed sets with zero. Math. Slovaca 45 (1) (1995) 9-17.
  11. R. Halas and J. Rachunek, Polars and prime ideals in ordered sets, Discuss. Math., Algebra and Stochastic Methods 15 (1995) 43-59.
  12. B. B. N. Koguep and C. Lele, On fuzzy prime ideals of lattices, SJPAM 3(2008) 1-11.
  13. J. N. Mordeson and D. S. Malik, Fuzzy Commutative Algebra, World Sci. Publ.,Singapore, 1998.
  14. T. Ramarao, C. P. Rao, D. Solomon and D. Abeje, Fuzzy Ideals and Filters of lattices, Asian Journal of Current Engineering and Maths. 2 (2013) 297-300.
  15. M. H. Stone, The theory of representations for Boolean algebras. Trans. Amer. Math. Soc. 40 (1936) 37-111.
  16. 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
  17. P. V. Venkataranasimhan, Pseudo-complements in posets. Proc. Amer. Math. Soc. 28 (1971) 9-17. https://doi.org/10.1090/S0002-9939-1971-0272687-X
  18. P. V. Venkataranasimhan, Semi-ideals in posets. Math. Ann. 185 (1970) 338-348. https://doi.org/10.1007/BF01349957
  19. 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
  20. L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965) 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X

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