Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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SOME PROPERTIES OF FUZZY LATTICES AS FUZZY RELATIONS

  • Chon, Inheung (Department of Mathematics Seoul Women's University)
  • Received : 2016.05.21
  • Accepted : 2016.09.11
  • Published : 2016.09.30
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Abstract

We define a fuzzy lattice as a fuzzy relation, prove the distributive inequalities and the modular inequality of fuzzy lattices, and show that the fuzzy totally ordered set is a distributive fuzzy lattice and that the distributive fuzzy lattice is modular.

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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. I. Chon, Fuzzy lattices as fuzzy relations, Korean J. Math. 23 (2015), 557-569. https://doi.org/10.11568/kjm.2015.23.4.557
  3. I. Chon, Fuzzy partial order relations and fuzzy lattices, Korean J. Math. 17 (2009), 361-374.
  4. J. A. Goguen, L-fuzzy sets, J. Math. Anal. Appl. 18 (1967), 145-174. https://doi.org/10.1016/0022-247X(67)90189-8
  5. E. Sanchez, Resolution of composite fuzzy relation equation, Inform. and control 30 (1976), 38-48. https://doi.org/10.1016/S0019-9958(76)90446-0
  6. P. Venugopalan, Fuzzy ordered sets, Fuzzy sets and systems 46 (1992), 221-226. https://doi.org/10.1016/0165-0114(92)90134-P
  7. L. A. Zadeh, Fuzzy sets, Inform. and control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  8. L. A. Zadeh, Similarity relations and fuzzy orderings, Inform. Sci. 3 (1971), 177-200. https://doi.org/10.1016/S0020-0255(71)80005-1