Research Article

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

by  Dr. M. Marudai, V. Rajendran
journal cover
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 24 - Issue 7
Published: June 2011
Authors: Dr. M. Marudai, V. Rajendran
10.5120/2950-3963
PDF

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 },
                        year    = { 2011 },
                        volume  = { 24 },
                        number  = { 7 },
                        pages   = { 26-32 },
                        doi     = { 10.5120/2950-3963 },
                        publisher = { Foundation of Computer Science (FCS), NY, USA }
                        }
                        %0 Journal Article
                        %D 2011
                        %A Dr. M. Marudai
                        %A V. Rajendran
                        %T Intuitionistic Fuzzy Equipotent Sublattices of Lattice Ordered Groups with Respect to S-Norms%T 
                        %J International Journal of Computer Applications
                        %V 24
                        %N 7
                        %P 26-32
                        %R 10.5120/2950-3963
                        %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
  • K. Atanassov, Intuitionistic fuzzy sets, Fuzzy sets and systems, 20 (1986), pp. 87-96.
  • N. Ajmal, the lattice of fuzzy normal sub groups is modular, Inform. Sci. 83 (1995), pp. 199-209.
  • N. Ajmal and K.V. Thomas, The lattice of fuzzy sub-groups and fuzzy normal sub-groups, Inform. Sci., 76 (1994), pp. 1 – 11.
  • 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.
  • B. Banerjee and D.Kr. Basnet, Intuitionstic fuzzy sub rings and ideals, J. Fuzzy Math. 11 (1) (2003), pp. 139-155.
  • R. Biswas, Insuitionstic fuzzy subrings, Mathematical Forum x(1989), pp. 37-46.
  • H. Bustince and P. Butillo, Structures on intuitionistic fuzzy relations, Fuzzy sets and systems 78 (1996), pp. 293 – 303.
  • D. Coker and A. Hayder Es, On fuzzy compactness in intuitionistic fuzzy topological spaces, J. Fuzzy Math. 3 (1995), 899 – 909.
  • D. Coker. An introduction to intuitionistic fuzzy topological spaces, Fuzzy sets and systems 88 (1997), pp. 81 – 89.
  • J.A. Goguen, L-fuzzy sets, J. Math Anal. Appl 18, pp. 145-174 (1967).
  • H. Gurcay, D. Coker and A. Haydar Es, on fuzzy continuity in intuitionistic fuzzy topological spaces, J. fuzzy Maths. 5 (1997), pp. 365-378.
  • 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.
  • 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.
  • K. Har, S.Y. Jang and H.W. Kang, Intuitionistic fuzzy sub groups and Cosets, Honam Math. J. 26 (1) (2004), pp. 17-41.
  • K. Hur, Y.B. Jun and J.H. Ryou, Intuitionistic fuzzy topological groups, Honam Math. J. 26 (2) (2004), pp. 163-192.
  • S.J. Lee and E.P. Lee, The categoris of Intuitionistic fuzzy topological spaces, Bull. Korean Math Soc. 37 (1) (2000), pp. 63-76.
  • T.K. Mukharjee and M.K. Sen, on fuzzy ideals of a ring 1, Fuzzy sets and systems 21 (1987), pp. 98 – 104.
  • 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.
  • 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.
  • Nanda. S, Fuzzy Lattices, Bulletin of Calcutta Math. Soc. 18 (1989), pp.1 – 2.
  • A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971), pp. 512 – 517.
  • G.S.V. Satya Saibaba, Fuzzy lattice ordered groups, South East Asian Bulletin of Mathamatics 32, pp. 749 – 766 (2008).
  • K.V. Thomas and Latha. S. Nair, Rough ideals in a lattice, International Journal fuzzy systems and rough systems. (To appear).
  • 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.
  • Wang-Jin Liu, Fuzzy invariant sub groups and fuzzy ideals, Fuzzy sets and systems 8 (1982), pp. 133 – 139.
  • 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.
  • L.A. Zadeh, Fuzzy sets, Inform and control 8 (1965), pp. 338 – 353.
Index Terms
Computer Science
Information Sciences
No index terms available.
Keywords

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

Powered by PhDFocusTM