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http://dx.doi.org/10.5391/IJFIS.2014.14.2.154

Lattices of Interval-Valued Fuzzy Subgroups  

Lee, Jeong Gon (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University)
Hur, Kul (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University)
Lim, Pyung Ki (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University)
Publication Information
International Journal of Fuzzy Logic and Intelligent Systems / v.14, no.2, 2014 , pp. 154-161 More about this Journal
Abstract
We discuss some interesting sublattices of interval-valued fuzzy subgroups. In our main result, we consider the set of all interval-valued fuzzy normal subgroups with finite range that attain the same value at the identity element of the group. We then prove that this set forms a modular sublattice of the lattice of interval-valued fuzzy subgroups. In fact, this is an interval-valued fuzzy version of a well-known result from classical lattice theory. Finally, we employ a lattice diagram to exhibit the interrelationship among these sublattices.
Keywords
Interval-valued fuzzy set; Interval-valued fuzzy subgroup; Interval-valued fuzzy normal subgroup; Level subset; Modular lattice;
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Times Cited By KSCI : 13  (Citation Analysis)
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