摘要
文[2]首次提出了未确知性信息的基本概念及其数学处理途径,开辟了一个全新的研究领域.本文在[2]的基本上,提出了未确知测度和信比测度的概念,为未确知性信息的数学处理提出了一种测度式的理论框架.特别地,还证明了:如果基本空间X 是可数的,则未确知数{X,F(x)}的信比之和小于或等于1.在数值特征上揭示了未确知信息与随机性信息和模糊性信息的明显区别,从理论上证明了文[12]中给出的未确知性信息这一概念的合理性。
In the paper[2],the concept of unascertainty and the ways of treating itmathematically were proposed for the first time.The paper showed the readers anew field of research.In this paper,unascertained measure and faith ratio measureare defined on the basis of the paper[2].There measures provide us with a basicframe of mathematical theory on the basis of the theory of measure.Particularly,we prove that:If the basic space X is countable,the total faith ratio of{X,F(x)}is less than or equal to 1.This shows the obvious differences between unascertaintyand randomness,and also fuzziness.It proves theoretically that,the concept pro-posed in the paper[2] is reasonable.
关键词
未确知信息
信比测定
未确知数
unascertained information
unascertained measure
faith ratio measure
unascertained number
faith distribution
