On(∈,∈∨q(λ, μ))-fuzzy LI-ideals in lattice implication algebras
- LIU Chun-hui
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(2):
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Firstly, the notion of (∈,∈∨q(λ, μ))-fuzzy LI-ideals in lattice implication algebras is further studied, and some new properties and equivalent characterizations of (∈,∈∨q(λ, μ))-fuzzy LI-ideals 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 LI-ideal 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 LI-ideals with respect to a fixed pair(λ, μ)in a given lattice implication algebra, under the partial order, forms a complete distributive lattice.