[0,∞)区间的N范数及广义自相关系数k的计算方法

N-Norm on [0,∞) and Method for Calculating Generalized Self-Correlation Coefficient k

三角范数理论中的N范数(N-norm)是柔性逻辑中非运算的数学模型。在柔性逻辑学研究中,模糊命题和它的模糊非命题之间的相关性用连续变化的广义自相关系数k∈[0,1]来刻画。非算子是随广义自相关系数k的变化而连续变化的算子簇。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,文章以三角范数作为柔性逻辑研究的数学工具,定义了[0,∞)区间上的N范数、N性生成元和N性生成函数,并研究了相关主要性质;证明了N范数生成定理;讨论了广义自相关系数的计算;给出了由N性生成函数直接生成N范数、计算不动点l和计算广义自相关系数k的方法。为[0,∞)区间上的连接词运算模型提供了数学生成方法。

N-norm in triangular norm theory is the mathematical model of NOT operator in flexible logic.The correlation between each fuzzy proposition and its corresponding fuzzy NOT proposition is described by a continuously changeable generalized self-correlation coefficient k∈.NOT operator is a continuously changeable operator cluster with continuous change of k.In the real world,many logic reasoning controls must be accomplished respectively in their own definition domains.This paper uses triangular norm theory as an important mathematical tool to study the flexible logic on interval [0,∞）.N-norm,N generator and N generating function are defined and their related main properties are studied.Generation theorem of N-norm is proven.The method of generating N-norm,that of calculating fixed point l and that of calculating generalized self-correlation coefficient are provided.These research results provide the important theoretical base for the construction of propositional connective model on [0,∞） interval.