B-模糊集合代数和广义互信息公式

B-fuzzy Set Algebra and a General Cross-information Equation

基于两种概率的区分,推导出了一个广义Shannon熵公式和一个广义互信息公式。后者和模糊性有关,并且可用于语言和感觉中的信息度量。为了由原子语句为真的条件概率求出复合语句为真的条件概率,提出了一个遵循布尔运算的模糊集合代数。所谓的模糊信息被还原为概率信息。新的理论在经典理论——概率论,集合论及Shannon信息论——的基础上容易理解。

Based on the distinction between two types of probabillities of sentences, a general Shannon entropy equation and a general Shannon cross-entropy equation are deduced. The later is related to fuzziness and can be used to measure information in language and sensation. To calculate the condition probability of a compound sentence from those of atomic sentences, a fuzzy set algebra following Boolean operations is proposed. So-called fuzzy information is reduced into probability information. The new theory can be easily understood on basis of classical theories: the probability theory, the set theory, and the Shannon information theory.