In this paper, we defined the concept of implicative and fuzzy implicative ideals of lattice implication algebras, and discussed the properties of them. And then, we pointed out the relations between implicative ideal...In this paper, we defined the concept of implicative and fuzzy implicative ideals of lattice implication algebras, and discussed the properties of them. And then, we pointed out the relations between implicative ideal and LI _ideal, implicative iedal and implicative filter, implicative ideal and fuzzy implicative ideal, fuzzy implicative ideal and fuzzy implicative filter, and fuzzy implicative ideal and fuzzy LI _ideal.展开更多
In this paper, some necessary and sufficient conditions that a finite lattice implication algebra is simple are established. Specially, it is proved that a finite lattice implication algebra L is simple if and only if...In this paper, some necessary and sufficient conditions that a finite lattice implication algebra is simple are established. Specially, it is proved that a finite lattice implication algebra L is simple if and only if （L, ≤） is a chain, if and only if there exists the unique dual atom in L. Also, it is given that a finite lattice implication algebra with order of a prime number is simple.展开更多
This paper is devoted to the study of some properties of fuzzy filters in lattice implication algebras. The structure theorem of fuzzy filters and the category of the sets of fuzzy filters were established with some b...This paper is devoted to the study of some properties of fuzzy filters in lattice implication algebras. The structure theorem of fuzzy filters and the category of the sets of fuzzy filters were established with some basic properties of it were discussed.展开更多
文摘In this paper, we defined the concept of implicative and fuzzy implicative ideals of lattice implication algebras, and discussed the properties of them. And then, we pointed out the relations between implicative ideal and LI _ideal, implicative iedal and implicative filter, implicative ideal and fuzzy implicative ideal, fuzzy implicative ideal and fuzzy implicative filter, and fuzzy implicative ideal and fuzzy LI _ideal.
基金Supported by a grant of Natural Science Foundation of Guangdong Province in China（021073）
文摘In this paper, some necessary and sufficient conditions that a finite lattice implication algebra is simple are established. Specially, it is proved that a finite lattice implication algebra L is simple if and only if （L, ≤） is a chain, if and only if there exists the unique dual atom in L. Also, it is given that a finite lattice implication algebra with order of a prime number is simple.
文摘This paper is devoted to the study of some properties of fuzzy filters in lattice implication algebras. The structure theorem of fuzzy filters and the category of the sets of fuzzy filters were established with some basic properties of it were discussed.
