Study on the properties of A-subset
Xiqing Long, Hua Zhu, Yang Xu · Journal of Intelligent & Fuzzy Systems · 2017
The concept of A-subset is introduced in lattice implication algebras. Firstly, the properties of the A-subset are discussed when A is a general set of lattice implication algebras. Next, the properties of A-subset are investigated when the A is an LI-ideal of lattice implication algebras. We obtain some properties of A-subset and prove that B(A)(the A-subset of B) is an LI-ideal in lattice implication algebras. Finally, the properties of A-subset are investigated in lattice implication product algebras. We prove that the A-subset of ∏ i = 1 n B i is the product of A-subset of B i ( i = 1, 2, ⋯ , n ) respectively ( ( ∏ i = 1 n B i ) ( ∏ i = 1 n A i ) = ( ∏ i = 1 n B i ( A i ) ) ) .