中介真值程度的度量及其应用(I)  

Measure of Medium Truth Scale and Its Application (I)

作　　者：洪龙[1] 肖奚安[2] 朱梧槚[1] 

机构地区：[1]南京航空航天大学信息科学与技术学院 [2]中国人民解放军理工大学理学院,南京210016

出　　处：《计算机学报》2006年第12期2186-2193,共8页Chinese Journal of Computers

基　　金：国家'九七三'重点基础研究发展规划项目基金(G1999032701);国家自然科学基金(60273037)资助~~

摘　　要：以中介数学系统为背景,为处理工程实践和科学研究中普遍存在的模糊现象提供一种度量逻辑真值程度的方法.在建立了谓词的ε标准度概念后,描述了对一般应用的数值区域与对应谓词的真值之间的关系;采用距离概念,并以对应谓词真值的数值区域的长度为基准,定义了距离比率函数及距离比率的特殊变换,并由此建立了一维情形下个体真值程度函数.又在提出关于n维情形的分支谓词、幂集逆映射和标准度向量概念后,描述了真值程度和函数、极值分支函数等n维情形的应用形式.应用示例表明:由于提出超态概念,所以理论上能把真值程度域从[0,1]拓宽到(-∞,+∞);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.因此,真值程度的度量将在涉及模糊现象的领域得到有效的应用.To process fuzzy phenomenon existed widely in engineering and scientific research, a new method with measuring logic truth scale, having background of medium mathematics system, is proposed. After establishing about ε standard pointer of the predicate, the relation between truths of the predicate and areas of numerical value of general application is described. Adopting the concept of distance and using length of numerical value interval to different predicate truths as norm, thereby the function of distance ratio and its special transformation are defined, and from this the individual truth grad function in one-dimensional is found. Additional, the ramification predicate about n-dimensional, the inverse mapping of power set and the vector of standard pointer are advanced to describe the application form in n-dimensional, such as the sum function of truth grad, polar value branch function and so on. The given demonstrations show that the interval of truth scale can be expended from [0,1] to （-∞,＋∞） in theory with the concept of super-truth advanced in this paper, and the definition of truth grade function possesses quantitative form processed by computers and features of objective property and universal adaptability. Consequently, the method of measure of medium truth scale will find efficacious application in fields dealing with vague phenomenon.

关 键 词：模糊现象 度量 真值程度 应用 中介数学系统 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]