• Kim, Seon-Yu (Department of Mathematics Education and Institute of Mathematics Education, Chinju National University of Education) ;
  • Roh, Eun-Hwan (Department of Mathematics Education and Institute of Mathematics Education, Chinju National University of Education)
  • Received : 2009.06.01
  • Accepted : 2009.08.07
  • Published : 2009.09.25


We introduce the concepts of a fuzzifying filter and a fuzzifying implicative filter in lattice implication algebras.


  1. K. M. Abd El-Hakeim and F. M. Zeyada, Some bifuzzy topologies induced by a fuzzifying topology: Part (I): Fundamental Concepts, J. Fuzzy Math. 8(4) (2000), 845-856.
  2. H. M. Ghanim, F. A. Ibrahim and M. A. Sakr, On fuzzifying filters, grills and basic proximities, J. Fuzzy Math. 8(1) (2000), 79-87.
  3. S. Y. Kim, E. H. Roh and Y. B. Jun. On ultrefilters of lattice implication algebras, Scientiae Mathematicae 2 (1998), 201-204.
  4. J. Lin and Y. Xu, Filters and structure of lattice implication algebra, Chinese Science Bulletin 42(18) (1997), 1517-1520.
  5. J. Liu and Y. Xu, On prim e filters and decomposition theorem of lattice implication algebras, J. Fuzzy Math. 6(4) (1998), 1001-1008.
  6. E. H. Roh. S. Y. Kim. Y. Xu and Y. B. Jun, Some operations on lattice implication algebras. International J. of Mathematics and Mathematical Sciences 27(1) (2001), 45-52.
  7. J. B. Rosser and A. R. Turquette, Many-Valued Logics, North-Holland, Amsterdam-New York. 1952.
  8. E. H. Roh, Y. Xu and K. Y. Qin, On implicative filters of lattice implication algebras, Submitted.
  9. Y. Xu, Lattice implication algebras, J. of Southwest Jiaotong Univ. 28(1) (1993), 20-27. (Chinese)
  10. Y. Xu and K. Y. Qin, On filters of lattice implication algebras. J. Fuzzy Math. 1 (1993), 251-260.
  11. Y. Xu. K. Y. Qin and E. H. Roh, On prime filters of lattice H implication algebras, J. Fuzzy Math. 9(3) (2001), 583-588.
  12. Y. Xu. E. H. Roh and K. Y. Qin On quotient lattice implication algebras induced by fuzzy filters, J. Fuzzy Math. 9(3) (2001), 611-617.
  13. Ming Sheng Ying, A new approach for fuzzy topology I, Fuzzy Sets and Systems 39 (1991), 303-321.
  14. J. Z. Shell. Fuzzifying groups based on complete residuated lattice-valued logic, Information Sciences 75 (1993) 165-186.
  15. L. A. Zadeh, Fuzzy sets, Inform. Control. 8 (1965), 338-353.
  16. G. J. Zhang, Semi-open sets and semi-continuity in fuzzifying topological spaces, J. Fuzzy Math. 8(4) (2000), 981-987.
  17. X. F. Zou and J. Z. Shen, Fuzzifying codes and fuzzifying prefix codes, J. Fuzzy Math. 8(2) (2000), 307-313.