Affiliations: Department of Mathematics, Northwest University, Xi'an, P.R. China | Academy of Bordeaux, University of Pau, Bordeaux, France
Note: [] Corresponding author. Xiaolong Xin, Department of Mathematics, Northwest University, Xi'an 710127, P.R. China. Tel.: +86 13571952880, E-mail: xlxin@nwu.edu.cn
Abstract: In the present paper we give a procedure by which we generate a fuzzy ideal (resp. a fuzzy filter and a convex fuzzy sublattice) by a fuzzy set in a lattice. And we prove that a convex fuzzy sublattice generated by a fuzzy set is an intersection of a fuzzy ideal and a fuzzy filter generated by the same fuzzy set in a lattice. Moreover, the homomorphic image and pre-image of a fuzzy ideal (fuzzy filter and convex fuzzy sublattice) generated by a fuzzy set are studied. In particular, we prove that the set of convex fuzzy sublattices of a modular lattice can form a modular lattice. Finally, as an application of our main result, we give an interesting example in BCK-algebras.
