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- 2018
关于格蕴涵代数的(∈,∈∨q(λ, μ))-模糊LI-理想
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Abstract:
摘要： 首先, 对格蕴涵代数的(∈,∈∨q(λ, μ))-模糊LI-理想概念作进一步深入研究, 获得了(∈,∈∨q(λ, μ))-模糊LI-理想的一些新的性质和刻画。 其次, 在由给定的格蕴涵代数L上全体模糊集构成的集合上定义了一个偏序关系, 利用给出了由L上的一个模糊集生成的(∈,∈∨q(λ, μ))-模糊LI-理想的定义并建立了其表示定理。 最后, 证明了L关于给定偶对(λ, μ)的全体(∈,∈∨q(λ, μ))-模糊LI-理想之集在偏序下构成一个完备的分配格。
Abstract: 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
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