任意区间上的广义N范数与生成元

Generalized N-Norm and N-Generator on Any Interval

在泛逻辑的不确定性推理中,N范数是一级运算的数理模型。论文目的是对现有泛逻辑中[0,1]区间上的N范数及其生成元进行扩展和完善,称任意[a,b]区间为广义区间,首先定义了广义区间[a,b]上的广义N范数与广义N性生成元;研究了它们的主要性质:封闭性、不动点、泛非性、偶等性等,给出了N性生成元的分类:常规N性生成元、奇异N性生成元、中心对称N性生成元;最后得到并证明了重要的广义N性生成元生成定理和广义N范数生成定理,从而为任意区间[a,b]上的分数逻辑的连接词运算模型提供了数学生成方法。

The mathematical results of this paper have already been used in computation on AI (artificial intelligence) logic reasoning in the first author's Ph.D dissertation at Northwestern Polytechnical University. In the process of uncertainties reasoning with universal logic, N-norm is the mathematical model of the first level operation. N-norm and N-generator are defined on interval [0,1]. We extend and improve the existing N-norm and TV-generator based on [0,1] interval in universal logic. Any interval [a, b] is called generalized interval here. We first give the definitions of generalized N-norm and generalized N-generator on generalized interval [a, b], then study their main properties: closeness, fixed point, universal not property, even equivalent property, etc. Then we give the classifications: normal TV-generator, strange TV-generator, center symmetrical TV-generator. Finally we prove the important generating theorem of generalized TV-generator and that of generalized TV-norm.