未确知信息及其数学处理

在本文中,“未确知信息”被定义为由于条件的限制,在进行决策时必须利用、但尚无法确知的信息,也就是说,它是由于决策者所掌握的证据尚不足以确定事物的真实状态和数量关系,而带来的纯主观的认识上的不确定性。本文指出,不确定性信息可以分为强和弱二类:随机性和模糊性是强不确定性信息;未确知性是弱不确定性信息。未确知性的“弱”表现在两方面;首先,当未确知性与随机性和模糊性共存时,它就被后二者所掩盖或包含;其次,当未确知性单独存在时,它可以用主观概率和主观隶属度来描述,也就是采用随机性和模糊性的表达方式来表达。这样,未确知性的数学处理就得到了极大的简化,主观概率分布和主观隶属度分布可统一为信比分布。文中给出了确定信比分布的途径。此外,本文还提出了“未确知数”的概念和定义。

Unascertamed Information and Its Mathematical Treatment

In this paper unasoertained information is defined as the information that must It is pointed out in this paper,that the unascertamty is a kind of weak uncertainty compared with randomness and fuzziness,which are two kinds of strong uncertainty.The weakness of unascertainty is presented in two aspects.First,if ascertainty is accompamed by randomness or fuzziness,it will be hidden or can be contained by them Second,if there is only unascertainty,it can be expressed by subjective probability distribution or subjective membership function That is to say,it can be described in the same manner as randomness or fuzziness.In this way,the mathematical treatment of unascertamed information is greatly simplified. Subjective probability distribution and subjective membership function can be unified by faith function.The way to obtain the faith function of unascertained information is also presented.In addition,the concept and definition of unascertained number are proposed in the paper.