一类模糊逻辑系统幺半群与同态映射

首先利用代数中幺半群的概念给出了模糊逻辑系统专业领域的概念, 建立专业领域概念的目的是为了规范模糊逻辑系统中语言变量的取值范围, 从而将模糊逻辑系统看作是某个笛卡儿乘积幺半群的有限子集. 然后利用这个笛卡儿乘积幺半群的乘积运算构造了模糊逻辑系统幺半群. 最后, 在一定的约定条件下证明了通常使用的一类Mamdani形模糊逻辑系统的输出可以看作是从模糊逻辑系统幺半群到连续函数域的同态映射.

A Class of Monoids of Fuzzy Logic Systems and Homomorphic Mapping

The concept "specialized field" is proposed for fuzzy logic systems based on the concept of monoid in mathematical algebraic, which is utilized to provide the value ranges of the language variables in fuzzy logic systems. From above, a fuzzy logic system can be regarded as a finite sub-set in a Cartesian product monoid. Then the monoid of fuzzy logic systems is constructed using the product operation in the Cartesian product monoid. Finally, it is proved that the outputs of a class of used Mamdani fuzzy logic systems is the homomorphic mapping from the monoid of fuzzy logic systems into the continuous function domain.