Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ON INTERVAL-VALUED FUZZY LATTICES

  • LEE, JEONG GON (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University) ;
  • HUR, KUL (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University) ;
  • LIM, PYUNG KI (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University)
  • Received : 2014.12.22
  • Accepted : 2015.01.15
  • Published : 2015.06.25
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Abstract

We discuss the relationship between interval-valued fuzzy ideals and interval-valued fuzzy congruence on a distributive lattice L and show that for a generalized Boolean algebra the lattice of interval-valued fuzzy ideals is isomorphic to the lattice of interval-valued fuzzy congruences. Finally we consider the products of interval-valued fuzzy ideals and obtain a necessary and sufficient condition for an interval-valued fuzzy ideal on the direct sum of lattices to be representable as a direct sum of interval-valued fuzzy ideals on each lattice.

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References

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