[0,∞]区间N范数的定义及生成定理  

Definition of N-norm and it's Generation Theorem on [0,∞] Interval

作　　者：范艳峰[1,2] 何华灿[2] 

机构地区：[1]河南工业大学信息科学与工程学院,郑州450001 [2]西北工业大学计算机学院,西安710072

出　　处：《计算机科学》2010年第5期190-193,270,共5页Computer Science

基　　金：国家自然科学基金项目(No.60273087)"经验知识推理理论研究";北京市自然科学基金项目(No.4032009)"不精确推理理论研究";西北工业大学基础研究基金(No.W018101)资助

摘　　要：柔性逻辑学的研究目标是探索逻辑的一般规律,它指出命题真值误差用连续变化的广义自相关系数k∈[0,1]来刻画。在柔性逻辑的不确定推理中,N范数是一级运算的数理模型。由于在现实生活中,很多逻辑推理控制必须在其自身的定义域内完成,因此以三角范数作为柔性逻辑学研究的数学工具,定义了[0,∞]区间上的N范数和N性生成元,并研究了相关主要性质;证明了N范数生成定理;给出了广义自相关系数的计算方法;证明了[0,∞]区间上指数(幂)型N性生成元为N性生成元完整簇;从而为柔性逻辑中[0,∞]区间的一级运算模型提供了重要的理论基础。The research aim of flexible logics is to explore the general law of logic, it indicates that propositional truth value error is described by the continuously changeable generalized self-correlation coefficient k∈[0,∞].N-norm is the mathematic model of 1-level operation in uncertain reasoning. In the real world, many logic reasoning controls must be accomplished in the original true value domain. This paper used triangular norm theory as an important mathematical tool to study the flexible logics on interval[0,∞].N-norm and N-generator on[0,∞] were defined, and the relative main properties were studied. Generation theorem of N-norm was proven. Method for calculating generalized self-correlation coefficient k was given. The paper proved that exponential N-generator is N-generator integrity cluster on[0,∞].These researches provided the important theoretical base for 1-level operation model on[0,∞] interval in flexible logics

关 键 词：柔性逻辑 范数 生成元 广义自相关系数 生成元完整簇 

分 类 号：O152.7[理学—数学]