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Intuitionistic Fuzzy Equipotent Sublattices of Lattice Ordered Groups with Respect to S-Norms

by Dr. M. Marudai, V. Rajendran
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 24 - Number 7
Year of Publication: 2011
Authors: Dr. M. Marudai, V. Rajendran
10.5120/2950-3963

Dr. M. Marudai, V. Rajendran . Intuitionistic Fuzzy Equipotent Sublattices of Lattice Ordered Groups with Respect to S-Norms. International Journal of Computer Applications. 24, 7 ( June 2011), 26-32. DOI=10.5120/2950-3963

@article{ 10.5120/2950-3963,
author = { Dr. M. Marudai, V. Rajendran },
title = { Intuitionistic Fuzzy Equipotent Sublattices of Lattice Ordered Groups with Respect to S-Norms },
journal = { International Journal of Computer Applications },
issue_date = { June 2011 },
volume = { 24 },
number = { 7 },
month = { June },
year = { 2011 },
issn = { 0975-8887 },
pages = { 26-32 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume24/number7/2950-3963/ },
doi = { 10.5120/2950-3963 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:10:23.051050+05:30
%A Dr. M. Marudai
%A V. Rajendran
%T Intuitionistic Fuzzy Equipotent Sublattices of Lattice Ordered Groups with Respect to S-Norms
%J International Journal of Computer Applications
%@ 0975-8887
%V 24
%N 7
%P 26-32
%D 2011
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, we introduce the notion of intuitionistic fuzzy equipotent lattice in a fuzzy lattice and then some basic properties are investigated. Characterization of intuitionistic fuzzy equipotent lattices are given. Using a collection of lattices, an intuitionistic fuzzy equipotent lattice is established. The notion of fuzzy equipotent lattice relation on the family of all intuitionistic fuzzy sub lattices of L are discussed upper and lower level sets of fuzzy equipotent lattices are studied.

References
  1. K. Atanassov, Intuitionistic fuzzy sets, Fuzzy sets and systems, 20 (1986), pp. 87-96.
  2. N. Ajmal, the lattice of fuzzy normal sub groups is modular, Inform. Sci. 83 (1995), pp. 199-209.
  3. N. Ajmal and K.V. Thomas, The lattice of fuzzy sub-groups and fuzzy normal sub-groups, Inform. Sci., 76 (1994), pp. 1 – 11.
  4. N. Ajmal and K.V. Thomas, A complete study of the lattices of fuzzy congruence and fuzzy normal sub groups, Inform. Sci. 82 (1995), pp. 198-218.
  5. B. Banerjee and D.Kr. Basnet, Intuitionstic fuzzy sub rings and ideals, J. Fuzzy Math. 11 (1) (2003), pp. 139-155.
  6. R. Biswas, Insuitionstic fuzzy subrings, Mathematical Forum x(1989), pp. 37-46.
  7. H. Bustince and P. Butillo, Structures on intuitionistic fuzzy relations, Fuzzy sets and systems 78 (1996), pp. 293 – 303.
  8. D. Coker and A. Hayder Es, On fuzzy compactness in intuitionistic fuzzy topological spaces, J. Fuzzy Math. 3 (1995), 899 – 909.
  9. D. Coker. An introduction to intuitionistic fuzzy topological spaces, Fuzzy sets and systems 88 (1997), pp. 81 – 89.
  10. J.A. Goguen, L-fuzzy sets, J. Math Anal. Appl 18, pp. 145-174 (1967).
  11. H. Gurcay, D. Coker and A. Haydar Es, on fuzzy continuity in intuitionistic fuzzy topological spaces, J. fuzzy Maths. 5 (1997), pp. 365-378.
  12. K. Hur, S.Y. Jang and H.Kl. Kang, Intuitionistic fuzzy sub groupoids, International Journal of Fuzzy Logic and Intelligent systems 3 (1) (2003), 72-77.
  13. K. Hur, H.W. Kang and H.K. Song, Intuitionistic fuzzy sub groups and sub rings, Honam Math. J. 25 (1) (2003), pp. 19-41.
  14. K. Har, S.Y. Jang and H.W. Kang, Intuitionistic fuzzy sub groups and Cosets, Honam Math. J. 26 (1) (2004), pp. 17-41.
  15. K. Hur, Y.B. Jun and J.H. Ryou, Intuitionistic fuzzy topological groups, Honam Math. J. 26 (2) (2004), pp. 163-192.
  16. S.J. Lee and E.P. Lee, The categoris of Intuitionistic fuzzy topological spaces, Bull. Korean Math Soc. 37 (1) (2000), pp. 63-76.
  17. T.K. Mukharjee and M.K. Sen, on fuzzy ideals of a ring 1, Fuzzy sets and systems 21 (1987), pp. 98 – 104.
  18. M. Marudai and V. Rajendran, Characterization of fuzzy lattices on a group with respect to T-norms, International Journal of Computer Applications. (0975-8887) Volume 8 – No.8, October 2010. pp. 8 – 15.
  19. M. Marudai and V. Rajendran, Generalized product of fuzzy lattices and fuzzy ideals, Advances in Fuzzy Mathematics, (ISSN 0973-533x) Volume 6, Number 1 (2011), pp. 135 - 144.
  20. Nanda. S, Fuzzy Lattices, Bulletin of Calcutta Math. Soc. 18 (1989), pp.1 – 2.
  21. A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971), pp. 512 – 517.
  22. G.S.V. Satya Saibaba, Fuzzy lattice ordered groups, South East Asian Bulletin of Mathamatics 32, pp. 749 – 766 (2008).
  23. K.V. Thomas and Latha. S. Nair, Rough ideals in a lattice, International Journal fuzzy systems and rough systems. (To appear).
  24. K.V. Thomas and Latha. S. Nair, Rough intuitionistic fuzzy sets in a lattice, International Mathematical forum, Vol.6, 2011, No.27, pp. 1327 – 1335.
  25. Wang-Jin Liu, Fuzzy invariant sub groups and fuzzy ideals, Fuzzy sets and systems 8 (1982), pp. 133 – 139.
  26. Y.H. Yon and K.H. Kim, on intuitionistic fuzzy filters and ideals of lattices, Fat East J. Math, Sci 1(3), pp. 429 – 442.
  27. L.A. Zadeh, Fuzzy sets, Inform and control 8 (1965), pp. 338 – 353.
Index Terms

Computer Science
Information Sciences

Keywords

Fuzzy lattice Fuzzy equipotent Lattice level cut intuitionistic fuzzy equipotent sub lattice Homomorphism

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