Ideals and Filters in Neutrosophic Lattices

Ideals and Filters in Neutrosophic Lattices

In this paper, we give ideal and filter definitions for neutrosophic lattices for the first time. We extend neutrosophic ideals and filters of neutrosophic lattices to pure neutrosophic lattices to obtain more flexible definitions.

___

  • Cantor G., Ueber eine eigenschaft des inbegriffs aller reelen algebraischen zahlen, Journal für die Reine und Angewandte Mathematik, 77, 258–262, 1874.
  • Zadeh L.A., Fuzzy sets, Information and Control, 8(3), 338–353, 1965.
  • Atanassov K.T., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), 87–96, 1986.
  • Smarandache F., A unifying field in logics: Neutrosophic logic, Philosophy, 1999.
  • Birkhoff G., Lattice Theory, American Mathematical Society Colloquium Publications, XXV, 1967.
  • Kandasamy V., Smarandache F., Neutrosophic lattices, Neutrosophic Sets and Systems, 2, 42–47, 2013.
  • Parveen M. R., Sekar P., Neutrosophic semilattices and their properties, Neutrosophic Sets and Systems, 65, 2015.