一种新的中介真值程度的度量方法及模糊谓词的分解

One New Method of Measure of Medium Truth Scale and Decomposition of Fuzzy Predicate

以中介数学系统为背景,为处理现实生活中普遍存在的模糊现象提供一种度量逻辑真值程度的新方法。在建立了谓词的标准度概念后,描述了谓词的真值与对应的数值区域之间的关系;采用距离的概念,并以对应谓词真值的数值区域长度为基准,给出了一维情形下的个体真值程度函数以及基于真值程度函数的一元谓词的表示法。又在提出了λ-真值程度截集、数与谓词的乘积概念后,给出了关于一元模糊谓词的中介分解定理,从而建立了一元模糊谓词与清晰谓词间的量化关系。应用示例表明:真值程度函数的定义具有计算机可以处理的定量形式且具有客观性和普适性的特点。

To process fuzzy phenomenon existing widely in social life, one new method with measuring truth grade, having background of medium mathematics system, is proposed. After establishing standard pointer of the predicate, the relation between truths of the predicate and areas of numerical value is described. Adopting the concept of distance and using length of numerical value interval to discriminate predicate truths as norm, the individual truth grade function, on which the method of representation of one-variate predicate that is based,are presented. Additional, the ~, truth-grade-cut set and the product of number with the predicate are advanced to give medium decomposition theorem about one-variate fuzzy predicate. Hence the quantitative relation between one-variate fuzzy predicate and distinct predicate is con- structed. The given demonstration show that the definition of truth grade function possesses quantitative form processed by computers and features of objective property and universal adaptability.