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ON INTERVAL-VALUED FUZZY LATTICES
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  • Journal title : Honam Mathematical Journal
  • Volume 37, Issue 2,  2015, pp.187-205
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2015.37.2.187
 Title & Authors
ON INTERVAL-VALUED FUZZY LATTICES
LEE, JEONG GON; HUR, KUL; LIM, PYUNG KI;
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 Abstract
We discuss the relationship between interval-valued fuzzy ideals and interval-valued fuzzy congruence on a distributive lattice L and show that for a generalized Boolean algebra the lattice of interval-valued fuzzy ideals is isomorphic to the lattice of interval-valued fuzzy congruences. Finally we consider the products of interval-valued fuzzy ideals and obtain a necessary and sufficient condition for an interval-valued fuzzy ideal on the direct sum of lattices to be representable as a direct sum of interval-valued fuzzy ideals on each lattice.
 Keywords
interval-valued fuzzy sublattice;interval-valued fuzzy ideal;interval-valued fuzzy filter;interval-valued fuzzy congruence;
 Language
English
 Cited by
 References
1.
N. Ajmal and K. V. Thomas, Fuzzy lattices, Inform. Sci.79(1994), 271-291. crossref(new window)

2.
R. Biswas, Rosenfeld's fuzzy subgroups with interval-valued membership functions, Fuzzy set and Systems 63(1995), 87-90.

3.
J. Y. Choi, S. R. Kim and K. Hur, Interval-valued smooth topological spaces, Honam Math. J. 32(4)(2010), 711-738. crossref(new window)

4.
M. B. Gorzalczany, A method of inference in approximate reasoning based on interval-values fuzzy sets, Fuzzy sets and Systems 21(1987), 1-17. crossref(new window)

5.
G. Gratzer, General Lattice Theory, Academic Press (1978).

6.
K. Hur, J. G. Lee and J. Y. Choi, Interval-valued fuzzy relations, J. Korean Institute of Intelligent systems 19(3)(2009), 425-432. crossref(new window)

7.
H. W. Kang and K. Hur, Interval-valued fuzzy subgroups and rings, Honam. Math. J. 32(4)(2010), 593-617. crossref(new window)

8.
K. C. Lee, K. Hur and P. K. Lim, Interval-valued fuzzy subgroups and level subgroups, Honam Math. J. 35(3)(2013), 525-540. crossref(new window)

9.
T. K. Mondal and S. K. Samanta, Topology of interval-valued fuzzy sets, Indian J. Pure Appl. Math 30(1)(1999), 20-38.

10.
B. Yuan and W. Wu, Fuzzy ideals on a distributive lattice, Fuzzy Sets and Systems(1990)

11.
L. A. Zadeh, Fuzzy sets, Inform. and Control 8(1965), 338-353. crossref(new window)

12.
K. Hur, H. W. Kang and H. K. Song, The concept of a linguistic variable and its application to approximate reasoning I, Inform. Sci. 8(1975), 199-249. crossref(new window)