R_0代数公理系统的简化与独立性

Simplified axiom systems of R_0 algebras and independence

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 ,并证明了这两个特征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。

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.