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从判断到识别的定性映射模型与模糊人工神经元*

, PP. 35-46

Keywords: 性质命题判断,定性映射,w_内积变换,转化程度函数,人工神经元,模糊隶属度函数,模式识别

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Abstract:

将基于属性量质特征转化的性质命题判断抽象为一个以定性基准为参量的动态定性映射,给出定性基准分别为一个区间、区间向量和n维超平行体网格的定义,讨论加权w对定性基准的几何意义,定性映射和人工神经元的关系,以及(性质判断的)定性映射转化为(模式)识别映射的机制和条件.指出,加权w的实质是对定性基准中的n维超平行体实施一个旋转变换.因人工神经元可看作是对n维超平行体的一个面实施加权w内积旋转变换后的形式,故是(加权w内积变换)定性映射的一个特例.当定性基准中n维超平行体的所有边长都趋近于零时,以(近)零边长的n维超平行体为基准的定性映射转化为一个向量的判断或搜索映射,并可对任一可转化为一个向量的模式进行识别.此外,本文还提出了属性量质转化程度函数的概念和一种导致定性基准边界模糊化的机制,指出,若用某个模糊化的转化程度函数代替定性映射进行判断和识别,则得到一种模糊判断和识别,并以一系列实例证实了定性映射和转化程度函数方法的实用性.

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