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INTUITIONISTIC FUZZY (t, s)-CONGRUENCES

  • Ahn Tae-Chon (School of Electrical Electronic and Information Engineering Wonkwang University) ;
  • Hur Kul (Division of Mathematics and Informational Statistic Wonkwang University) ;
  • Roh Seok-Beom (School of Electrical Electronic and Information Engineering Wonkwang University)
  • Published : 2006.06.01

Abstract

We introduce the notion of intuitionistic fuzzy (t, s)-congruences on a lattice and study some of its properties. Moreover, we obtain some properties of intuitionistic fuzzy congruences on the direct product of two lattices. Finally, we prove that the set of all intuitionistic fuzzy congruences on a lattice forms a distributive lattice.

Keywords

References

  1. K.Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20(1986),87-96 https://doi.org/10.1016/S0165-0114(86)80034-3
  2. Baldev Banerjee and Dhiren Kr. Basnet, Intuitionistic fuzzy subrings and ideals, J.Fuzzy Math. 11(1)(2003), 139-155
  3. R.Biswas, Intuitionistic fuzzy subgroups, Mathematical Forum x(1989), 37-46
  4. H.Bustince and P. Burillo, Structures on intuitionistic fuzzy relations, Fuzzy Sets and Systems 78(1996), 293-303 https://doi.org/10.1016/0165-0114(96)84610-0
  5. D. Coker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems 88(1997), 81-89 https://doi.org/10.1016/S0165-0114(96)00076-0
  6. D. Coker and A.Haydar Es, On fuzzy compactness in intuitionistic fuzzy topological spaces, J. Fuzzy Math. 3(1995),899-909
  7. G.Deschrijver and E.E.Kerre, On the composition of intuitionistic fuzzy relations, Fuzzy Sets and Systems 136(2003),333-361 https://doi.org/10.1016/S0165-0114(02)00269-5
  8. G.Gratzer, Lattice Theory, First concepts and Distributive lattices, W.H.Freemann and Company, San Francisco (1971)
  9. H.Gurcay, D. Coker and A.Haydar Es, On fuzzy continuity in intuitionistic fuzzy topological spaces, J.Fuzzy Math. 5(1997),365-378
  10. K.Hur, S.Y.Jang and H.W.Kang,Intuitionistic fuzzy subgroupoids, International Journal of Fuzzy Logic and Intelligent Systems 3(1) (2003), 72-77 https://doi.org/10.5391/IJFIS.2003.3.1.072
  11. K.Hur, H.W.Kang and H.K.Song, Intuitionistic fuzzy subgroups and subrings, Honam Mathematical J.25(1)(2003), 19-41
  12. K.Hur, S.Y.Jang and H.W.Kang, Intuitionistic fuzzy subgroups and cosets, Honam Math. J,26(1)(2004), 17-41
  13. K.Hur, Y.B.Jun and J.H.Ryou, Intuitionistic fuzzy topological groups, Honam Mathematical J.26(2)(2004),163-192
  14. K.Hur, J.H.Kim and J.H.Ryou, Intuitionistic fuzzy topological spaces, J.Korea Soc. Math.Educ.Ser.B : Pure Appl.Math.11(3)(2004), 243-265
  15. K.Hur, S.Y.Jang and H.W.Kang, Intuitionistic fuzzy normal subgroups and intuitionistic fuzzy cosets, Honam Math. J.26(4)(2004), 559-587
  16. K.Hur, S.Y.Jang and H.W.Kang, Intuitionistic fuzzy congruences on a lattice, J.Appl.Math.and Computing 18(12)( 2005), 465-486
  17. K.Hur, S.Y.Jang and H.W.Kang, Intuitionistic fuzzy equivalence relations, Honam Math. J.27(2)(2005), 163-181
  18. K.Hur, S.Y.Jang and Y.B.Jun, Intuitionistic fuzzy congruences, Far East J.Math. Sci.(FJMS) 17(1)(2005), 1-29
  19. S.J.Lee and E.P.Lee, The category of intuitionistic fuzzy topological spaces, Bull. Korean Math. Soc. 37(1)(2000),63-76
  20. B.Schweizer and A.Sklar, Statistical metric spaces, Pacific J.Math.10(1960), 313-334 https://doi.org/10.2140/pjm.1960.10.313
  21. F.I.Sidky and M.M.Atallah, On T-congruences of lattices, The J.Fuzzy Math.6(4)(1998),993-1000
  22. L.A.Zadeh, Fuzzy sets, Inform. and Control 8(1965), 338-353 https://doi.org/10.1016/S0019-9958(65)90241-X