双重不确定性信息的代数结构及运算

Algebraic Structure and Mathematical Computing of Double Uncertainty Information

从逻辑代数的角度研究了不确定性信息中以自然语言形式所刻画的随机信息和模糊信息,分别按照各自的序关系建立了自然语言形式的偏序集,形成了双重不确定性信息的笛卡尔积,并构造了能够同时处理这两类不确定性信息的格蕴涵代数;通过该格蕴涵代数上二元运算的定义,给出了双重不确定性信息间的一些常用运算,使得带有确定性数量值的双重不确定性信息可以直接进行自然语言间的运算,避免了信息处理过程中由信息转换而造成的信息损失。

From the perspective of logical algebra, this paper researched two kinds of uncertainty information -- random information and fuzzy information that are described by natural language, constructed the respective posets according to the ordering relations and formed a Cartesian product of the double uncertainty information. The lattice implication algebra was established for dealing with these two kinds of uncertainty information. Through the definitions of the binary operations on the lattice implication algebra, some common operations between the double uncertainty information are given, which made the double uncertainty information with the certainty number computing directly between natural language. And then, in the information processing, the loss avoided. of information caused by information comverting can be