The purpose of this paper is to further study the(∈,∈∨q_k)-fuzzy filter theory in R_0-algebras. Some new properties of(∈, ∈∨ q_k)-fuzzy filters are given. Representation theorem of(∈,∈∨q_k)-fuzzy filter which...The purpose of this paper is to further study the(∈,∈∨q_k)-fuzzy filter theory in R_0-algebras. Some new properties of(∈, ∈∨ q_k)-fuzzy filters are given. Representation theorem of(∈,∈∨q_k)-fuzzy filter which is generated by a fuzzy set is established. It is proved that the set consisting of all(∈, ∈∨q_k)-fuzzy filters on a given R_0-algebra, under the partial order, forms a complete distributive lattice.展开更多
In the present paper,some basic properties of MP filters of R0 algebra M are investigated.It is proved that ■ is a bounded distributive lattice by introducing the negation operator,the meet operator ∧,the join opera...In the present paper,some basic properties of MP filters of R0 algebra M are investigated.It is proved that ■ is a bounded distributive lattice by introducing the negation operator,the meet operator ∧,the join operator ∨ and the implication operator → on the set FMP(M) of all MP filters of M.Moreover,some conditions under which ■ is an R0 algebra are given.And the relationship between prime elements of FMP(M) and prime filters of M is studied.Finally,some equivalent characterizations of prime elements of FMP(M) are obtained.展开更多
基金Supported by Higher School Research Foundation of Inner Mongolia(NJSY14283)
文摘The purpose of this paper is to further study the(∈,∈∨q_k)-fuzzy filter theory in R_0-algebras. Some new properties of(∈, ∈∨ q_k)-fuzzy filters are given. Representation theorem of(∈,∈∨q_k)-fuzzy filter which is generated by a fuzzy set is established. It is proved that the set consisting of all(∈, ∈∨q_k)-fuzzy filters on a given R_0-algebra, under the partial order, forms a complete distributive lattice.
文摘In the present paper,some basic properties of MP filters of R0 algebra M are investigated.It is proved that ■ is a bounded distributive lattice by introducing the negation operator,the meet operator ∧,the join operator ∨ and the implication operator → on the set FMP(M) of all MP filters of M.Moreover,some conditions under which ■ is an R0 algebra are given.And the relationship between prime elements of FMP(M) and prime filters of M is studied.Finally,some equivalent characterizations of prime elements of FMP(M) are obtained.
