赋范格H蕴涵代数和模糊格H蕴涵代数

Normed Lattice H Implication Algebras and Fuzzy Lattice H Implication Algebras

在范数的条件下扩充了格H蕴涵代数的概念,即赋范格H蕴涵代数,并讨论一些性质。然后将模糊集合论运用于赋范格H蕴涵代数,给出了模糊赋范格H蕴涵代数的定义,得到了一些基本性质。通过使用两个赋范格H蕴涵代数之间的映射定义了赋范格H蕴涵代数同态,且得到了一些性质。最后得到了在赋范格H蕴涵代数中的数列对于蕴涵距离是有界的结论。

Extended the notion of lattice H implication algebra L under a norm situation （i. e. , normed lattice H implication algebras）, and some properties were discussed. At the other hand, by applying the fuzzy set concept to normed lattice H implication algebras, introduced the notion of fuzzy normed lattice H implication algebras and discussed some of the basic properties. Defined a normed lattice H implication homomorphism by use of a mapping f which has two normed lattice H implication algebras L1 and L2, and obtain its properties. It is shown that sequences operations to implication distance in a normed lattice H implication algebra are bounded.