R0代数公理系统的简化与独立性

研究了一类重要的模糊逻辑代数系统－－R0代数，给出了R0代数一系列基本性质及与其它一些模糊逻辑代数系统之间的关系，讨论了R0代数公理系统的简化问题，得到R0代数的两个特征定理，并证明了这两个特下定理中条件的独立性，由此得到R0代数两个独立的公理系统，研究结果表明，R0代数类和弱R0代数类都构成代数簇，即等式代数类，因而这两个代数类关于子代数、同态像以及直积是封闭的。

Simplified axiom systems of R0 algebras and independence

The R 0 algebras are further studied because they are a kind of important algebra systems in fuzzy logic, and a series of basic properties of R 0 algebras are given out. Two characterization theorems of R 0 algebras are obtained, and the independence of the conditions in two characterization theorems are discussed, so two independent axiom systems of R 0 algebras are obtained. According to these results, both R 0 algebras and weak R 0 algebras form algebraic varieties, i.e., equation algebraic classes. Hence, these classes of algebras are closed under sub_algebras , homomorphic images and direct products. In addition, the relationships among R 0 algebras and some other algebra systems in fuzzy logic are also discussed.