算子模糊命题逻辑中公式恒真恒假水平的模型

为了在模糊推理中求得公式为真程度的下界和上界,算子模糊逻辑显示使用0,1]区间中的实数作为算子描述模糊命题的可信程度,其公式的语义值可以在公式的恒真水平和恒假水平之间变动。基于算子模糊命题逻辑,证明了任意公式在二值解释的意义下都可以转化成与之等值的合取范式和析取范式,并根据公式的合取范式或析取范式给出了公式恒真水平和恒假水平模型的生成方法。公式的恒真水平和恒假水平在根本上决定了公式的语义性质,其模型给出了公式在何时达到其最小和最大语义值的一个解答。

Model generation of formula truth level in propositional operator fuzzy logic

T o f ind the upper bo und and low er bound for the t ruth level of the formula in oper ato r fuzzy log ic, the uncer tainty of a fuzzy proposit ion is ex plicit ly represented by an operator which is a real number in the interval f rom 0 to 1. Thus a g iven formula varies in semant ic v alue f rom its minimum to it s max imum. Based on pr opo sit io nal operato r fuzzy log ic, the concept s of t ruth level and false level of a g iv en fo rmula w ere def ined to char acterize it s minimal and max imal semant ic values, and how a fo rmula reached it s t ruth level and false level w as discussed. Under the semant ics o f two-value interpretatio n, it is show n that the formula can be tr ansformed equivalent ly to a co njunct iv e normal form o r a disjunct ive no rmal fo rm, so that the model of the truth level and that o f the false level can be obtained easily. Then the semant ic properties of the fo rmula w ere clearly determined