
On(∈,∈∨q_{(λ, μ)})fuzzy LIideals in lattice implication algebras
 LIU Chunhui

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(2):
6572.
doi:10.6040/j.issn.16719352.0.2017.508

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Firstly, the notion of (∈,∈∨q_{(λ, μ)})fuzzy LIideals in lattice implication algebras is further studied, and some new properties and equivalent characterizations of (∈,∈∨q_{(λ, μ)})fuzzy LIideals are given. Secondly, a partial order is defined on the set of all fuzzy sets in a given lattice implication algebra L, the definition of (∈,∈∨q_{(λ, μ)})fuzzy LIideal which is generated by a fuzzy set is given and its representation theorem is established by using. Finally, It is proved that the set consisting of all (∈,∈∨q_{(λ, μ)})fuzzy LIideals with respect to a fixed pair(λ, μ)in a given lattice implication algebra, under the partial order, forms a complete distributive lattice.